%% %% This is file `mandi.sty', %% generated with the docstrip utility. %% %% The original source files were: %% %% mandi.dtx (with options: `package') %% %% Copyright (C) 2018 by Paul J. Heafner %% --------------------------------------------------------------------------- %% This work may be distributed and/or modified under the conditions of the %% LaTeX Project Public License, either version 1.3 of this license or (at %% your option) any later version. The latest version of this license is in %% http://www.latex-project.org/lppl.txt %% and version 1.3 or later is part of all distributions of LaTeX version %% 2005/12/01 or later. %% %% This work has the LPPL maintenance status `maintained'. %% %% The Current Maintainer of this work is Paul J. Heafner. %% %% This work consists of the files mandi.dtx %% mandi.ins %% mandi.pdf %% README %% %% and includes the derived files mandi.sty %% vdemo.py. %% --------------------------------------------------------------------------- %% %%\ProvidesPackage{mandi}[2019/01/12 2.7.5 Macros for physics and astronomy] \NeedsTeXFormat{LaTeX2e}[1999/12/01] \RequirePackage{amsmath} \RequirePackage{amssymb} \RequirePackage{array} \RequirePackage{cancel} \RequirePackage[dvipsnames]{xcolor} \RequirePackage{enumitem} \RequirePackage{environ} \RequirePackage{esint} \RequirePackage[g]{esvect} \RequirePackage{etoolbox} \RequirePackage{filehook} \RequirePackage{extarrows} \RequirePackage{float} \RequirePackage[T1]{fontenc} \RequirePackage{graphicx} \RequirePackage{epstopdf} \RequirePackage{textcomp} \RequirePackage{letltxmacro} \RequirePackage{listings} \RequirePackage{mathtools} \RequirePackage[framemethod=TikZ]{mdframed} \RequirePackage{stackengine} \RequirePackage{suffix} \RequirePackage{tensor} \RequirePackage{xargs} \RequirePackage{xparse} \RequirePackage{xspace} \RequirePackage{ifthen} \RequirePackage{calligra} \RequirePackage[hypertexnames=false]{hyperref} \hypersetup{colorlinks=true,urlcolor=blue} \DeclareMathAlphabet{\mathcalligra}{T1}{calligra}{m}{n} \DeclareFontShape{T1}{calligra}{m}{n}{<->s*[2.2]callig15}{} \DeclareGraphicsRule{.tif}{png}{.png}{`convert #1 `basename #1 .tif`.png} \DeclareMathAlphabet{\mathpzc}{OT1}{pzc}{m}{it} \usetikzlibrary{shadows} \definecolor{vbgcolor}{rgb}{1,1,1} % background for code listings \definecolor{vshadowcolor}{rgb}{0.5,0.5,0.5} % shadow for code listings \lstdefinestyle{vpython}{% % style for code listings language=Python,% % select language morekeywords={__future__,division,append, % VPython/GlowScript specific keywords arange,arrow,astuple,axis,background,black,blue,cyan,green,% magenta,orange,red,white,yellow,border,box,color,comp,% cone,convex,cross,curve,cylinder,degrees,diff_angle,dot,ellipsoid,extrusion,faces,% font,frame,graphs,headlength,height,headwidth,helix,index,interval,label,length,% line,linecolor,mag,mag2,make_trail,material,norm,normal,objects,opacity,points,pos,% print,print_function,proj,pyramid,radians,radius,rate,retain,ring,rotate,scene,% shaftwidth,shape,sign,size,space,sphere,text,trail_object,trail_type,True,twist,up,% vector,visual,width,offset,yoffset,GlowScript,VPython,vpython,trail_color,% trail_radius,pps,clear,False,CoffeeScript,graph,gdisplay,canvas,pause,vec,clone,% compound,vertex,triangle,quad,attach_trail,attach_arrow,textures,bumpmaps,% print_options,get_library,read_local_file},% captionpos=b,% % position caption frame=shadowbox,% % shadowbox around listing rulesepcolor=\color{vshadowcolor},% % shadow color basicstyle=\footnotesize,% % basic font for code listings commentstyle=\bfseries\color{red}, % font for comments keywordstyle=\bfseries\color{blue},% % font for keywords showstringspaces=true,% % show spaces in strings stringstyle=\bfseries\color{green},% % color for strings numbers=left,% % where to put line numbers numberstyle=\tiny,% % set to 'none' for no line numbers xleftmargin=20pt,% % extra left margin backgroundcolor=\color{vbgcolor},% % some people find this annoying upquote=true,% % how to typeset quotes breaklines=true}% % break long lines \definecolor{formcolor}{gray}{0.90} % color for form background \newcolumntype{C}[1]{>{\centering}m{#1}} \newboolean{@optromanvectors} \newboolean{@optboldvectors} \newboolean{@optsinglemagbars} \newboolean{@optbaseunits} \newboolean{@optdrvdunits} \newboolean{@optaltnunits} \newboolean{@optapproxconsts} \newboolean{@optuseradians} \setboolean{@optromanvectors}{false} % this is where you set the default option \setboolean{@optboldvectors}{false} % this is where you set the default option \setboolean{@optsinglemagbars}{false} % this is where you set the default option \setboolean{@optbaseunits}{false} % this is where you set the default option \setboolean{@optdrvdunits}{true} % this is where you set the default option \setboolean{@optaltnunits}{false} % this is where you set the default option \setboolean{@optapproxconsts}{false} % this is where you set the default option \setboolean{@optuseradians}{false} % this is where you set the default option \DeclareOption{romanvectors}{\setboolean{@optromanvectors}{true}} \DeclareOption{boldvectors}{\setboolean{@optboldvectors}{true}} \DeclareOption{singlemagbars}{\setboolean{@optsinglemagbars}{true}} \DeclareOption{baseunits}{\setboolean{@optbaseunits}{true}} \DeclareOption{drvdunits}{\setboolean{@optdrvdunits}{true}} \DeclareOption{approxconsts}{\setboolean{@optapproxconsts}{true}} \DeclareOption{useradians}{\setboolean{@optuseradians}{true}} \ProcessOptions\relax \newcommand*{\mandiversion}{\ifmmode% 2.7.5\mbox{ dated }2019/01/12% \else% 2.7.5 dated 2019/01/12% \fi }% \typeout{ } \typeout{mandi: You're using mandi version \mandiversion.} \@ifpackageloaded{amssymb}{% \csundef{square} \typeout{mandi: Package amssymb detected. Its \protect\square\space has been redefined.} }{% \typeout{mandi: Package amssymb not detected.} }% \newcommand*{\per}{\ensuremath{/}} \newcommand*{\usk}{\ensuremath{\cdot}} \newcommand*{\unit}[2]{\ensuremath{{#1}\;{#2}}} \newcommand*{\ampere}{\ensuremath{\mathrm{A}}} \newcommand*{\arcminute}{\ensuremath{'}} \newcommand*{\arcsecond}{\ensuremath{''}} \newcommand*{\atomicmassunit}{\ensuremath{\mathrm{u}}} \newcommand*{\candela}{\ensuremath{\mathrm{cd}}} \newcommand*{\coulomb}{\ensuremath{\mathrm{C}}} \newcommand*{\degree}{\ensuremath{^{\circ}}} \newcommand*{\electronvolt}{\ensuremath{\mathrm{eV}}} \newcommand*{\eV}{\electronvolt} \newcommand*{\farad}{\ensuremath{\mathrm{F}}} \newcommand*{\henry}{\ensuremath{\mathrm{H}}} \newcommand*{\hertz}{\ensuremath{\mathrm{Hz}}} \newcommand*{\hour}{\ensuremath{\mathrm{h}}} \newcommand*{\joule}{\ensuremath{\mathrm{J}}} \newcommand*{\kelvin}{\ensuremath{\mathrm{K}}} \newcommand*{\kilogram}{\ensuremath{\mathrm{kg}}} \newcommand*{\metre}{\ensuremath{\mathrm{m}}} \newcommand*{\minute}{\ensuremath{\mathrm{min}}} \newcommand*{\mole}{\ensuremath{\mathrm{mol}}} \newcommand*{\newton}{\ensuremath{\mathrm{N}}} \newcommand*{\ohm}{\ensuremath{\Omega}} \newcommand*{\pascal}{\ensuremath{\mathrm{Pa}}} \newcommand*{\radian}{\ensuremath{\mathrm{rad}}} \newcommand*{\second}{\ensuremath{\mathrm{s}}} \newcommand*{\siemens}{\ensuremath{\mathrm{S}}} \newcommand*{\steradian}{\ensuremath{\mathrm{sr}}} \newcommand*{\tesla}{\ensuremath{\mathrm{T}}} \newcommand*{\volt}{\ensuremath{\mathrm{V}}} \newcommand*{\watt}{\ensuremath{\mathrm{W}}} \newcommand*{\weber}{\ensuremath{\mathrm{Wb}}} \newcommand*{\C}{\coulomb} \newcommand*{\F}{\farad} \newcommand*{\J}{\joule} \newcommand*{\N}{\newton} \newcommand*{\Pa}{\pascal} \newcommand*{\rad}{\radian} \newcommand*{\sr}{\steradian} \newcommand*{\T}{\tesla} \newcommand*{\V}{\volt} \newcommand*{\W}{\watt} \newcommand*{\Wb}{\weber} \newcommand*{\square}[1]{\ensuremath{{#1}^2}} % prefix 2 \newcommand*{\cubic}[1]{\ensuremath{{#1}^3}} % prefix 3 \newcommand*{\quartic}[1]{\ensuremath{{#1}^4}} % prefix 4 \newcommand*{\reciprocal}[1]{\ensuremath{{#1}^{-1}}} % prefix -1 \newcommand*{\reciprocalsquare}[1]{\ensuremath{{#1}^{-2}}} % prefix -2 \newcommand*{\reciprocalcubic}[1]{\ensuremath{{#1}^{-3}}} % prefix -3 \newcommand*{\reciprocalquartic}[1]{\ensuremath{{#1}^{-4}}} % prefix -4 \newcommand*{\squared}{\ensuremath{^2}} % postfix 2 \newcommand*{\cubed}{\ensuremath{^3}} % postfix 3 \newcommand*{\quarted}{\ensuremath{^4}} % postfix 4 \newcommand*{\reciprocaled}{\ensuremath{^{-1}}} % postfix -1 \newcommand*{\reciprocalsquared}{\ensuremath{^{-2}}} % postfix -2 \newcommand*{\reciprocalcubed}{\ensuremath{^{-3}}} % postfix -3 \newcommand*{\reciprocalquarted}{\ensuremath{^{-4}}} % postfix -4 \newcommand*{\emptyunit}{\ensuremath{\Box}} \newcommand*\mi@exchangeargs[2]{#2#1}% \newcommand*\mi@name{}% \long\def\mi@name#1#{\romannumeral0\mi@innername{#1}}% \newcommand*\mi@innername[2]{% \expandafter\mi@exchangeargs\expandafter{\csname#2\endcsname}{#1}}% \begingroup \@firstofone{% \endgroup \newcommand*\mi@forkifnull[3]{% \romannumeral\iffalse{\fi\expandafter\@secondoftwo\expandafter% {\expandafter{\string#1}\expandafter\@secondoftwo\string}% \expandafter\@firstoftwo\expandafter{\iffalse}\fi0 #3}{0 #2}}}% \newcommand*\selectbaseunit[3]{#1} \newcommand*\selectdrvdunit[3]{#2} \newcommand*\selectaltnunit[3]{#3} \newcommand*\selectunit{} \newcommand*\perpusebaseunit{\let\selectunit=\selectbaseunit} \newcommand*\perpusedrvdunit{\let\selectunit=\selectdrvdunit} \newcommand*\perpusealtnunit{\let\selectunit=\selectaltnunit} \newcommand*\hereusebaseunit[1]{% \begingroup\perpusebaseunit#1\endgroup}% \newcommand*\hereusedrvdunit[1]{% \begingroup\perpusedrvdunit#1\endgroup}% \newcommand*\hereusealtnunit[1]{% \begingroup\perpusealtnunit#1\endgroup}% \newenvironment{usebaseunit}{\perpusebaseunit}{}% \newenvironment{usedrvdunit}{\perpusedrvdunit}{}% \newenvironment{usealtnunit}{\perpusealtnunit}{}% \newcommand*\newphysicsquantity{\definephysicsquantity{\newcommand}} \newcommand*\redefinephysicsquantity{\definephysicsquantity{\renewcommand}} \newcommandx*\definephysicsquantity[5][4=,5=]{% \innerdefinewhatsoeverquantityfork{#3}{#4}{#5}{#1}{#2}{}{[1]}{##1}}% \newcommand*\newphysicsconstant{\definephysicsconstant{\newcommand}} \newcommand*\redefinephysicsconstant{\definephysicsconstant{\renewcommand}} \newcommandx*\definephysicsconstant[7][6=,7=]{% \innerdefinewhatsoeverquantityfork{#5}{#6}{#7}{#1}{#2}{#3}{}{#4}}% \newcommand*\innerdefinewhatsoeverquantityfork[3]{% \expandafter\innerdefinewhatsoeverquantity\romannumeral0% \mi@forkifnull{#3}{\mi@forkifnull{#2}{{#1}}{{#2}}{#1}}% {\mi@forkifnull{#2}{{#1}}{{#2}}{#3}}{#1}}% \newcommand*\innerdefinewhatsoeverquantity[8]{% \mi@name#4{#5}#7{\unit{#8}{\selectunit{#3}{#1}{#2}}}% \mi@name#4{#5baseunit}#7{\unit{#8}{#3}}% \mi@name#4{#5drvdunit}#7{\unit{#8}{#1}}% \mi@name#4{#5altnunit}#7{\unit{#8}{#2}}% \mi@name#4{#5onlyunit}{\selectunit{#3}{#1}{#2}}% \mi@name#4{#5onlybaseunit}{\ensuremath{#3}}% \mi@name#4{#5onlydrvdunit}{\ensuremath{#1}}% \mi@name#4{#5onlyaltnunit}{\ensuremath{#2}}% \mi@name#4{#5value}#7{\ensuremath{#8}}% \mi@forkifnull{#7}{% \ifx#4\renewcommand\mi@name\let{#5mathsymbol}=\relax\fi \mi@name\newcommand*{#5mathsymbol}{\ensuremath{#6}}}{}}% \ifthenelse{\boolean{@optboldvectors}} {\typeout{mandi: You'll get bold vectors.}} {\ifthenelse{\boolean{@optromanvectors}} {\typeout{mandi: You'll get Roman vectors.}} {\typeout{mandi: You'll get italic vectors.}}} \ifthenelse{\boolean{@optsinglemagbars}} {\typeout{mandi: You'll get single magnitude bars.}} {\typeout{mandi: You'll get double magnitude bars.}} \ifthenelse{\boolean{@optbaseunits}} {\perpusebaseunit % \typeout{mandi: You'll get base units.}} {\ifthenelse{\boolean{@optdrvdunits}} {\perpusedrvdunit % \typeout{mandi: You'll get derived units.}} {\perpusealtnunit % \typeout{mandi: You'll get alternate units.}}} \ifthenelse{\boolean{@optapproxconsts}} {\typeout{mandi: You'll get approximate constants.}} {\typeout{mandi: You'll get precise constants.}} \ifthenelse{\boolean{@optuseradians}} {\typeout{mandi: You'll get radians in ang mom, ang impulse, and torque.}} {\typeout{mandi: You won't get radians in ang mom, ang impulse, and torque.}} \typeout{ } \ifthenelse{\boolean{@optapproxconsts}} {\newcommand*{\mi@p}[2]{#1}} % approximate value {\newcommand*{\mi@p}[2]{#2}} % precise value \newcommand*{\m}{\metre} \newcommand*{\kg}{\kilogram} \newcommand*{\s}{\second} \newcommand*{\A}{\ampere} \newcommand*{\K}{\kelvin} \newcommand*{\mol}{\mole} \newcommand*{\cd}{\candela} \newcommand*{\dimdisplacement}{\ensuremath{\mathrm{L}}} \newcommand*{\dimmass}{\ensuremath{\mathrm{M}}} \newcommand*{\dimduration}{\ensuremath{\mathrm{T}}} \newcommand*{\dimcurrent}{\ensuremath{\mathrm{I}}} \newcommand*{\dimtemperature}{\ensuremath{\mathrm{\Theta}}} \newcommand*{\dimamount}{\ensuremath{\mathrm{N}}} \newcommand*{\dimluminous}{\ensuremath{\mathrm{J}}} \newcommand*{\infeet}[1]{\unit{#1}{\mathrm{ft}}} \newcommand*{\infeetpersecond}[1]{\unit{#1}{\mathrm{ft}\per\s}} \newcommand*{\infeetpersecondsquared}[1]{\unit{#1}{\mathrm{ft}\per\s\squared}} \newcommand*{\indegrees}[1]{\unit{#1}{\mkern-\thickmuskip\degree}} \newcommand*{\inFarenheit}[1]{\unit{#1}{\mkern-\thickmuskip\degree\mathrm{F}}} \newcommand*{\inCelsius}[1]{\unit{#1}{\mkern-\thickmuskip\degree\mathrm{C}}} \newcommand*{\inarcminutes}[1]{\unit{#1}{\mkern-\thickmuskip\arcminute}} \newcommand*{\inarcseconds}[1]{\unit{#1}{\mkern-\thickmuskip\arcsecond}} \newcommand*{\ineV}[1]{\unit{#1}{\electronvolt}} \newcommand*{\ineVocs}[1]{\unit{#1}{\mathrm{eV}\per c^2}} \newcommand*{\ineVoc}[1]{\unit{#1}{\mathrm{eV}\per c}} \newcommand*{\inMeV}[1]{\unit{#1}{\mathrm{MeV}}} \newcommand*{\inMeVocs}[1]{\unit{#1}{\mathrm{MeV}\per c^2}} \newcommand*{\inMeVoc}[1]{\unit{#1}{\mathrm{MeV}\per c}} \newcommand*{\inGeV}[1]{\unit{#1}{\mathrm{GeV}}} \newcommand*{\inGeVocs}[1]{\unit{#1}{\mathrm{GeV}\per c^2}} \newcommand*{\inGeVoc}[1]{\unit{#1}{\mathrm{GeV}\per c}} \newcommand*{\inamu}[1]{\unit{#1}{\mathrm{u}}} \newcommand*{\ingram}[1]{\unit{#1}{\mathrm{g}}} \newcommand*{\ingrampercubiccm}[1]{\unit{#1}{\mathrm{g}\per\cubic\mathrm{cm}}} \newcommand*{\inAU}[1]{\unit{#1}{\mathrm{AU}}} \newcommand*{\inly}[1]{\unit{#1}{\mathrm{ly}}} \newcommand*{\incyr}[1]{\unit{#1}{c\usk\mathrm{year}}} \newcommand*{\inpc}[1]{\unit{#1}{\mathrm{pc}}} \newcommand*{\insolarL}[1]{\unit{#1}{\Lsolar}} \newcommand*{\insolarT}[1]{\unit{#1}{\Tsolar}} \newcommand*{\insolarR}[1]{\unit{#1}{\Rsolar}} \newcommand*{\insolarM}[1]{\unit{#1}{\Msolar}} \newcommand*{\insolarF}[1]{\unit{#1}{\Fsolar}} \newcommand*{\insolarf}[1]{\unit{#1}{\fsolar}} \newcommand*{\insolarMag}[1]{\unit{#1}{\Magsolar}} \newcommand*{\insolarmag}[1]{\unit{#1}{\magsolar}} \newcommand*{\insolarD}[1]{\unit{#1}{\Dsolar}} \newcommand*{\insolard}[1]{\unit{#1}{\dsolar}} \newcommand*{\velocityc}[1]{\ensuremath{#1c}} \newcommand*{\lorentzfactor}[1]{\ensuremath{#1}} \newcommand*{\speed}{\velocity} \newphysicsquantity{displacement}% {\m}% [\m]% [\m] \newphysicsquantity{mass}% {\kg}% [\kg]% [\kg] \newphysicsquantity{duration}% {\s}% [\s]% [\s] \newphysicsquantity{current}% {\A}% [\A]% [\A] \newphysicsquantity{temperature}% {\K}% [\K]% [\K] \newphysicsquantity{amount}% {\mol}% [\mol]% [\mol] \newphysicsquantity{luminous}% {\cd}% [\cd]% [\cd] \newphysicsquantity{planeangle}% {\m\usk\reciprocal\m}% [\rad]% [\rad] \newphysicsquantity{solidangle}% {\m\squared\usk\reciprocalsquare\m}% [\sr]% [\sr] \newphysicsquantity{velocity}% {\m\usk\reciprocal\s}% [\m\usk\reciprocal\s]% [\m\per\s] \newphysicsquantity{acceleration}% {\m\usk\s\reciprocalsquared}% [\N\per\kg]% [\m\per\s\squared] \newphysicsquantity{gravitationalfield}% {\m\usk\s\reciprocalsquared}% [\N\per\kg]% [\N\per\kg] \newphysicsquantity{gravitationalpotential}% {\square\m\usk\reciprocalsquare\s}% [\J\per\kg]% [\J\per\kg] \newphysicsquantity{momentum}% {\m\usk\kg\usk\reciprocal\s}% [\N\usk\s]% [\kg\usk\m\per\s] \newphysicsquantity{impulse}% {\m\usk\kg\usk\reciprocal\s}% [\N\usk\s]% [\N\usk\s] \newphysicsquantity{force}% {\m\usk\kg\usk\s\reciprocalsquared}% [\N]% [\N] \newphysicsquantity{springstiffness}% {\kg\usk\s\reciprocalsquared}% [\N\per\m]% [\N\per\m] \newphysicsquantity{springstretch}% {\m}% []% [] \newphysicsquantity{area}% {\m\squared}% []% [] \newphysicsquantity{volume}% {\cubic\m}% []% [] \newphysicsquantity{linearmassdensity}% {\reciprocal\m\usk\kg}% [\kg\per\m]% [\kg\per\m] \newphysicsquantity{areamassdensity}% {\m\reciprocalsquared\usk\kg}% [\kg\per\m\squared]% [\kg\per\m\squared] \newphysicsquantity{volumemassdensity}% {\m\reciprocalcubed\usk\kg}% [\kg\per\m\cubed]% [\kg\per\m\cubed] \newphysicsquantity{youngsmodulus}% {\reciprocal\m\usk\kg\usk\s\reciprocalsquared}% [\N\per\m\squared]% [\Pa] \newphysicsquantity{stress}% {\reciprocal\m\usk\kg\usk\s\reciprocalsquared}% [\N\per\m\squared]% [\Pa] \newphysicsquantity{pressure}% {\reciprocal\m\usk\kg\usk\s\reciprocalsquared}% [\N\per\m\squared]% [\Pa] \newphysicsquantity{strain}% {}% []% [] \newphysicsquantity{work}% {\m\squared\usk\kg\usk\s\reciprocalsquared}% [\J]% [\N\usk\m] \newphysicsquantity{energy}% {\m\squared\usk\kg\usk\s\reciprocalsquared}% [\J]% [\N\usk\m] \newphysicsquantity{power}% {\m\squared\usk\kg\usk\s\reciprocalcubed}% [\W]% [\J\per\s] \newphysicsquantity{specificheatcapacity}% {\J\per\K\usk\kg}% [\J\per\K\usk\kg]% [\J\per\K\usk\kg] \newphysicsquantity{angularvelocity}% {\rad\usk\reciprocal\s}% [\rad\per\s]% [\rad\per\s] \newphysicsquantity{angularacceleration}% {\rad\usk\s\reciprocalsquared}% [\rad\per\s\squared]% [\rad\per\s\squared] \newphysicsquantity{momentofinertia}% {\m\squared\usk\kg}% [\m\squared\usk\kg]% [\J\usk\s\squared] \ifthenelse{\boolean{@optuseradians}} {% \newphysicsquantity{angularmomentum}% {\m\squared\usk\kg\usk\reciprocal\s\usk\reciprocal\rad}% [\kg\usk\m\squared\per(\s\usk\rad)]% [\N\usk\m\usk\s\per\rad] \newphysicsquantity{angularimpulse}% {\m\squared\usk\kg\usk\reciprocal\s\usk\reciprocal\rad}% [\J\usk\s\per\rad]% [\N\usk\m\usk\s\per\rad] \newphysicsquantity{torque}% {\m\squared\usk\kg\usk\s\reciprocalsquared\usk\reciprocal\rad}% [\N\usk\m\per\rad]% [\J\per\rad] }% {% \newphysicsquantity{angularmomentum}% {\m\squared\usk\kg\usk\reciprocal\s}% [\kg\usk\m\squared\per\s]% [\N\usk\m\usk\s] \newphysicsquantity{angularimpulse}% {\m\squared\usk\kg\usk\reciprocal\s}% [\J\usk\s]% [\N\usk\m\usk\s] \newphysicsquantity{torque}% {\m\squared\usk\kg\usk\s\reciprocalsquared}% [\N\usk\m]% [\J] }% \newphysicsquantity{entropy}% {\m\squared\usk\kg\usk\s\reciprocalsquared\usk\reciprocal\K}% [\J\per\K]% [\J\per\K] \newphysicsquantity{wavelength}% {\m}% [\m]% [\m] \newphysicsquantity{wavenumber}% {\reciprocal\m}% [\per\m]% [\per\m] \newphysicsquantity{frequency}% {\reciprocal\s}% [\hertz]% [\hertz] \newphysicsquantity{angularfrequency}% {\rad\usk\reciprocal\s}% [\rad\per\s]% [\rad\per\s] \newphysicsquantity{charge}% {\A\usk\s}% [\C]% [\C] \newphysicsquantity{permittivity}% {\m\reciprocalcubed\usk\reciprocal\kg\usk\s\reciprocalquarted\usk\A\squared}% [\C\squared\per\N\usk\m\squared]% [\F\per\m] \newphysicsquantity{permeability}% {\m\usk\kg\usk\s\reciprocalsquared\usk\A\reciprocalsquared}% [\T\usk\m\per\A]% [\henry\per\m] \newphysicsquantity{electricfield}% {\m\usk\kg\usk\s\reciprocalcubed\usk\reciprocal\A}% [\N\per\C]% [\V\per\m] \newphysicsquantity{electricdipolemoment}% {\m\usk\s\usk\A}% [\C\usk\m]% [\C\usk\m] \newphysicsquantity{electricflux}% {\m\cubed\usk\kg\usk\s\reciprocalcubed\usk\reciprocal\A}% [\N\usk\m\squared\per\C]% [\V\usk\m] \newphysicsquantity{magneticfield}% {\kg\usk\s\reciprocalsquared\usk\reciprocal\A}% [\T]% [\N\per\C\usk(\m\per\s)] % also \Wb\per\m\squared \newphysicsquantity{magneticflux}% {\m\squared\usk\kg\usk\s\reciprocalsquared\usk\reciprocal\A}% [\T\usk\m\squared]% [\volt\usk\s] % also \Wb and \J\per\A \newphysicsquantity{cmagneticfield}% {\m\usk\kg\usk\s\reciprocalcubed\usk\reciprocal\A}% [\N\per\C]% [\V\per\m] \newphysicsquantity{linearchargedensity}% {\reciprocal\m\usk\s\usk\A}% [\C\per\m]% [\C\per\m] \newphysicsquantity{areachargedensity}% {\reciprocalsquare\m\usk\s\usk\A}% [\C\per\square\m]% [\C\per\square\m] \newphysicsquantity{volumechargedensity}% {\reciprocalcubic\m\usk\s\usk\A}% [\C\per\cubic\m]% [\C\per\cubic\m] \newphysicsquantity{mobility}% {\m\squared\usk\kg\usk\s\reciprocalquarted\usk\reciprocal\A}% [\m\squared\per\volt\usk\s]% [(\m\per\s)\per(\N\per\C)] \newphysicsquantity{numberdensity}% {\reciprocalcubic\m}% [\per\cubic\m]% [\per\cubic\m] \newphysicsquantity{polarizability}% {\reciprocal\kg\usk\s\quarted\usk\square\A}% [\C\usk\square\m\per\V]% [\C\usk\m\per(\N\per\C)] \newphysicsquantity{electricpotential}% {\square\m\usk\kg\usk\reciprocalcubic\s\usk\reciprocal\A}% [\V]% [\J\per\C] \newphysicsquantity{emf}% {\square\m\usk\kg\usk\reciprocalcubic\s\usk\reciprocal\A}% [\V]% [\J\per\C] \newphysicsquantity{dielectricconstant}% {}% []% [] \newphysicsquantity{indexofrefraction}% {}% []% [] \newphysicsquantity{relativepermittivity}% {}% []% [] \newphysicsquantity{relativepermeability} {}% []% [] \newphysicsquantity{energydensity}% {\m\reciprocaled\usk\kg\usk\reciprocalsquare\s}% [\J\per\cubic\m]% [\J\per\cubic\m] \newphysicsquantity{energyflux}% {\kg\usk\s\reciprocalcubed}% [\W\per\m\squared]% [\W\per\m\squared] \newphysicsquantity{momentumflux}% {\reciprocal\m\usk\kg\usk\s\reciprocalsquared}% [\N\per\m\squared]% [\N\per\m\squared] \newphysicsquantity{electroncurrent}% {\reciprocal\s}% [\ensuremath{\mathrm{e}}\per\s]% [\ensuremath{\mathrm{e}}\per\s] \newphysicsquantity{conventionalcurrent}% {\A}% [\A]% [\C\per\s] \newphysicsquantity{magneticdipolemoment}% {\square\m\usk\A}% [\A\usk\square\m]% [\J\per\T] \newphysicsquantity{currentdensity}% {\reciprocalsquare\m\usk\A}% [\A\per\square\m]% [\C\usk\s\per\square\m] \newphysicsquantity{capacitance}% {\reciprocalsquare\m\usk\reciprocal\kg\usk\quartic\s\usk\square\A}% [\F]% [\C\per\V] % also \C\squared\per\N\usk\m, \s\per\ohm \newphysicsquantity{inductance}% {\square\m\usk\kg\usk\reciprocalsquare\s\usk\reciprocalsquare\A}% [\henry]% [\volt\usk\s\per\A] % also \square\m\usk\kg\per\C\squared, \Wb\per\A \newphysicsquantity{conductivity}% {\reciprocalcubic\m\usk\reciprocal\kg\usk\cubic\s\usk\square\A}% [(\A\per\square\m)\per(\V\per\m)]% [\siemens\per\m] \newphysicsquantity{resistivity}% {\cubic\m\usk\kg\usk\reciprocalcubic\s\usk\reciprocalsquare\A}% [\ohm\usk\m]% [(\V\per\m)\per(\A\per\square\m)] \newphysicsquantity{resistance}% {\square\m\usk\kg\usk\reciprocalcubic\s\usk\reciprocalsquare\A}% [\ohm]% [\V\per\A] \newphysicsquantity{conductance}% {\reciprocalsquare\m\usk\reciprocal\kg\usk\cubic\s\usk\square\A}% [\A\per\V]% [\siemens] 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\newcommand*{\euonetwo}{\euk{12}} \newcommand*{\euonethree}{\euk{13}} \newcommand*{\euonefour}{\euk{14}} \newcommand*{\eutwoone}{\euk{21}} \newcommand*{\eutwotwo}{\euk{22}} \newcommand*{\eutwothree}{\euk{23}} \newcommand*{\eutwofour}{\euk{24}} \newcommand*{\euthreeone}{\euk{31}} \newcommand*{\euthreetwo}{\euk{32}} \newcommand*{\euthreethree}{\euk{33}} \newcommand*{\euthreefour}{\euk{34}} \newcommand*{\eufourone}{\euk{41}} \newcommand*{\eufourtwo}{\euk{42}} \newcommand*{\eufourthree}{\euk{43}} \newcommand*{\eufourfour}{\euk{44}} \newcommand*{\gzero}{\ensuremath{\boldsymbol{\gamma}_0}} \newcommand*{\gone}{\ensuremath{\boldsymbol{\gamma}_1}} \newcommand*{\gtwo}{\ensuremath{\boldsymbol{\gamma}_2}} \newcommand*{\gthree}{\ensuremath{\boldsymbol{\gamma}_3}} \newcommand*{\gfour}{\ensuremath{\boldsymbol{\gamma}_4}} \newcommand*{\gk}[1]{\ensuremath{\boldsymbol{\gamma}_{#1}}} \newcommand*{\g}{\gk} \newcommand*{\gzerozero}{\gk{00}} \newcommand*{\gzeroone}{\gk{01}} \newcommand*{\gzerotwo}{\gk{02}} \newcommand*{\gzerothree}{\gk{03}} \newcommand*{\gzerofour}{\gk{04}} \newcommand*{\goneone}{\gk{11}} \newcommand*{\gonetwo}{\gk{12}} \newcommand*{\gonethree}{\gk{13}} \newcommand*{\gonefour}{\gk{14}} \newcommand*{\gtwoone}{\gk{21}} \newcommand*{\gtwotwo}{\gk{22}} \newcommand*{\gtwothree}{\gk{23}} \newcommand*{\gtwofour}{\gk{24}} \newcommand*{\gthreeone}{\gk{31}} \newcommand*{\gthreetwo}{\gk{32}} \newcommand*{\gthreethree}{\gk{33}} \newcommand*{\gthreefour}{\gk{34}} \newcommand*{\gfourone}{\gk{41}} \newcommand*{\gfourtwo}{\gk{42}} \newcommand*{\gfourthree}{\gk{43}} \newcommand*{\gfourfour}{\gk{44}} \newcommand*{\guzero}{\ensuremath{\boldsymbol{\gamma}^0}} \newcommand*{\guone}{\ensuremath{\boldsymbol{\gamma}^1}} \newcommand*{\gutwo}{\ensuremath{\boldsymbol{\gamma}^2}} \newcommand*{\guthree}{\ensuremath{\boldsymbol{\gamma}^3}} \newcommand*{\gufour}{\ensuremath{\boldsymbol{\gamma}^4}} \newcommand*{\guk}[1]{\ensuremath{\boldsymbol{\gamma}^{#1}}} \newcommand*{\gu}{\guk} \newcommand*{\guzerozero}{\guk{00}} \newcommand*{\guzeroone}{\guk{01}} \newcommand*{\guzerotwo}{\guk{02}} \newcommand*{\guzerothree}{\guk{03}} \newcommand*{\guzerofour}{\guk{04}} \newcommand*{\guoneone}{\guk{11}} \newcommand*{\guonetwo}{\guk{12}} \newcommand*{\guonethree}{\guk{13}} \newcommand*{\guonefour}{\guk{14}} \newcommand*{\gutwoone}{\guk{21}} \newcommand*{\gutwotwo}{\guk{22}} \newcommand*{\gutwothree}{\guk{23}} \newcommand*{\gutwofour}{\guk{24}} \newcommand*{\guthreeone}{\guk{31}} \newcommand*{\guthreetwo}{\guk{32}} \newcommand*{\guthreethree}{\guk{33}} \newcommand*{\guthreefour}{\guk{34}} \newcommand*{\gufourone}{\guk{41}} \newcommand*{\gufourtwo}{\guk{42}} \newcommand*{\gufourthree}{\guk{43}} \newcommand*{\gufourfour}{\guk{44}} \ExplSyntaxOn % Vectors formated as in M\&I, written in LaTeX3 \NewDocumentCommand{\mivector}{ O{,} m o }% {% \mi_vector:nn { #1 } { #2 } \IfValueT{#3}{\;{#3}} }% \seq_new:N \l__mi_list_seq \cs_new_protected:Npn \mi_vector:nn #1 #2 {% \ensuremath{% \seq_set_split:Nnn \l__mi_list_seq { , } { #2 } \int_compare:nF { \seq_count:N \l__mi_list_seq = 1 } { \left\langle } \seq_use:Nnnn \l__mi_list_seq { #1 } { #1 } { #1 } \int_compare:nF { \seq_count:N \l__mi_list_seq = 1 } { \right\rangle } }% }% \ExplSyntaxOff \ExplSyntaxOn % Column and row vectors, written in LaTeX3 \seq_new:N \l__vector_arg_seq \cs_new_protected:Npn \vector_main:nnnn #1 #2 #3 #4 {% \seq_set_split:Nnn \l__vector_arg_seq { #3 } { #4 } \begin{#1matrix} \seq_use:Nnnn \l__vector_arg_seq { #2 } { #2 } { #2 } \end{#1matrix} }% \NewDocumentCommand{\rowvector}{ O{,} m } {% \ensuremath{ \vector_main:nnnn { p } { \,\, } { #1 } { #2 } }% }% \NewDocumentCommand{\colvector}{ O{,} m } {% \ensuremath{ \vector_main:nnnn { p } { \\ } { #1 } { #2 } }% }% \ExplSyntaxOff \newcommandx{\scompscvect}[2][1,usedefault]{% \ifthenelse{\equal{#1}{}}% {% \colvector{\msub{#2}{1},\msub{#2}{2},\msub{#2}{3}}% }% {% \colvector{\msub{#2}{0},\msub{#2}{1},\msub{#2}{2},\msub{#2}{3}}% }% }% \newcommandx{\scompsCvect}[2][1,usedefault]{% \ifthenelse{\equal{#1}{}}% {% \colvector{\msup{#2}{1},\msup{#2}{2},\msup{#2}{3}}% }% {% \colvector{\msup{#2}{0},\msup{#2}{1},\msup{#2}{2},\msup{#2}{3}}% }% }% \newcommandx{\scompsrvect}[2][1,usedefault]{% \ifthenelse{\equal{#1}{}}% {% \rowvector[,]{\msub{#2}{1},\msub{#2}{2},\msub{#2}{3}}% }% {% \rowvector[,]{\msub{#2}{0},\msub{#2}{1},\msub{#2}{2},\msub{#2}{3}}% }% }% \newcommandx{\scompsRvect}[2][1,usedefault]{% \ifthenelse{\equal{#1}{}}% {% \rowvector[,]{\msup{#2}{1},\msup{#2}{2},\msup{#2}{3}}% }% {% \rowvector[,]{\msup{#2}{0},\msup{#2}{1},\msup{#2}{2},\msup{#2}{3}}% }% }% \newcommand*{\anglebetween}[2]{\ensuremath{\theta_{\vect{#1},\vect{#2}}}} \newcommand*{\bra}[1]{\ensuremath{\left\langle{#1}\right\lvert}} \newcommand*{\ket}[1]{\ensuremath{\left\lvert{#1}\right\rangle}} \newcommand*{\bracket}[2]{\ensuremath{\left\langle{#1}\!\!\right.% \left\lvert{#2}\right\rangle}} \newphysicsconstant{oofpez}% {\ensuremath{\frac{1}{\phantom{_o}4\pi\epsilon_0}}}% {\mi@p{9}{8.9875517873681764}\timestento{9}}% {\m\cubed\usk\kg\usk\reciprocalquartic\s\usk\A\reciprocalsquared}% [\newton\usk\m\squared\per\coulomb\squared]% [\m\per\farad] \newphysicsconstant{oofpezcs}% {\ensuremath{\frac{1}{\phantom{_o}4\pi\epsilon_0 c^2\phantom{_o}}}}% {\tento{-7}}% {\m\usk\kg\usk\s\reciprocalsquared\usk\A\reciprocalsquared}% [\N\usk\s\squared\per\C\squared]% [\T\usk\m\squared] \newphysicsconstant{vacuumpermittivity}% {\ensuremath{\epsilon_0}}% {\mi@p{9.0}{8.854187817}\timestento{-12}}% {\m\reciprocalcubed\usk\reciprocal\kg\usk\s\quarted\usk\A\squared}% [\C\squared\per\N\usk\m\squared]% [\F\per\m] \newphysicsconstant{mzofp}% {\ensuremath{\frac{\phantom{_oo}\mu_0\phantom{_o}}{4\pi}}}% {\tento{-7}}% {\m\usk\kg\usk\s\reciprocalsquared\usk\A\reciprocalsquared}% [\tesla\usk\m\per\A]% [\henry\per\m] \newphysicsconstant{vacuumpermeability}% {\ensuremath{\mu_0}}% {4\pi\timestento{-7}}% {\m\usk\kg\usk\s\reciprocalsquared\usk\A\reciprocalsquared}% [\T\usk\m\per\A]% [\henry\per\m] \newphysicsconstant{boltzmann}% {\ensuremath{k_B}}% {\mi@p{1.4}{1.38064852}\timestento{-23}}% {\m\squared\usk\kg\usk\reciprocalsquare\s\usk\reciprocal\K}% [\J\per\K]% [\J\per\K] \newphysicsconstant{boltzmannineV}% {\ensuremath{k_B}}% {\mi@p{8.6}{8.6173303}\timestento{-5}}% {\eV\usk\reciprocal\K}% [\eV\per\K]% [\eV\per\K] \newphysicsconstant{stefanboltzmann}% {\ensuremath{\sigma}}% {\mi@p{5.7}{5.670367}\timestento{-8}}% {\kg\usk\s\reciprocalcubed\usk\K\reciprocalquarted}% [\W\per\m\squared\usk\K\quarted]% [\W\per\m\squared\usk\K\quarted] \newphysicsconstant{planck}% {\ensuremath{h}}% {\mi@p{6.6}{6.626070040}\timestento{-34}}% {\m\squared\usk\kg\usk\reciprocal\s}% [\J\usk\s]% [\J\usk\s] \newphysicsconstant{planckineV}% {\ensuremath{h}}% {\mi@p{4.1}{4.135667662}\timestento{-15}}% {\eV\usk\s}% [\eV\usk\s]% [\eV\usk\s] \newphysicsconstant{planckbar}% {\ensuremath{\hslash}}% {\mi@p{1.1}{1.054571800}\timestento{-34}}% {\m\squared\usk\kg\usk\reciprocal\s}% [\J\usk\s]% [\J\usk\s] \newphysicsconstant{planckbarineV}% {\ensuremath{\hslash}}% {\mi@p{6.6}{6.582119514}\timestento{-16}}% {\eV\usk\s}% [\eV\usk\s]% [\eV\usk\s] \newphysicsconstant{planckc}% {\ensuremath{hc}}% {\mi@p{2.0}{1.98644568}\timestento{-25}}% {\m\cubed\usk\kg\usk\reciprocalsquare\s}% [\J\usk\m]% [\J\usk\m] \newphysicsconstant{planckcineV}% {\ensuremath{hc}}% {\mi@p{1240}{1.23984193}\timestento{3}}% {\eV\usk\text{n}\m}% [\eV\usk\text{n}\m]% [\eV\usk\text{n}\m] \newphysicsconstant{rydberg}% {\ensuremath{\msub{R}{\infty}}}% {\mi@p{1.1}{1.0973731568508}\timestento{7}}% {\reciprocal\m}% [\reciprocal\m]% [\reciprocal\m] \newphysicsconstant{bohrradius}% {\ensuremath{a_0}}% {\mi@p{5.3}{5.2917721067}\timestento{-11}}% {\m}% [\m]% [\m] \newphysicsconstant{finestructure}% {\ensuremath{\alpha}}% {\mi@p{\frac{1}{137}}{7.2973525664\timestento{-3}}}% {}% []% [] \newphysicsconstant{avogadro}% {\ensuremath{N_A}}% {\mi@p{6.0}{6.022140857}\timestento{23}}% {\reciprocal\mol}% [\reciprocal\mol]% [\reciprocal\mol] \newphysicsconstant{universalgrav}% {\ensuremath{G}}% {\mi@p{6.7}{6.67408}\timestento{-11}}% {\m\cubed\usk\reciprocal\kg\usk\s\reciprocalsquared}% [\N\usk\m\squared\per\kg\squared]% [\J\usk\m\per\kg\squared] \newphysicsconstant{surfacegravfield}% {\ensuremath{g}}% {\mi@p{9.8}{9.807}}% {\m\usk\s\reciprocalsquared}% [\N\per\kg]% [\N\per\kg] \newphysicsconstant{clight}% {\ensuremath{c}}% {\mi@p{3}{2.99792458}\timestento{8}}% {\m\usk\reciprocal\s}% [\m\per\s]% [\m\per\s] \newphysicsconstant{clightinfeet}% {\ensuremath{c}}% {\mi@p{1}{0.983571}}% {\text{ft}\usk\reciprocal{\text{n}\s}}% [\text{ft}\per\text{n}\s]% [\text{ft}\per\mathrm{n}\s] \newphysicsconstant{Ratom}% {\ensuremath{r_{\text{atom}}}}% {\tento{-10}}% {\m}% [\m]% [\m] \newphysicsconstant{Mproton}% {\ensuremath{m_p}}% {\mi@p{1.7}{1.672621898}\timestento{-27}}% {\kg}% [\kg]% [\kg] \newphysicsconstant{Mneutron}% {\ensuremath{m_n}}% {\mi@p{1.7}{1.674927471}\timestento{-27}}% {\kg}% [\kg]% [\kg] \newphysicsconstant{Mhydrogen}% {\ensuremath{m_H}}% {\mi@p{1.7}{1.6737236}\timestento{-27}}% {\kg}% [\kg]% [\kg] \newphysicsconstant{Melectron}% {\ensuremath{m_e}}% {\mi@p{9.1}{9.10938356}\timestento{-31}}% {\kg}% [\kg]% [\kg] \newphysicsconstant{echarge}% {\ensuremath{e}}% {\mi@p{1.6}{1.6021766208}\timestento{-19}}% {\A\usk\s}% [\C]% [\C] \newphysicsconstant{Qelectron}% {\ensuremath{Q_e}}% {-\echargevalue}% {\A\usk\s}% [\C]% [\C] \newphysicsconstant{qelectron}% {\ensuremath{q_e}}% {-\echargevalue}% {\A\usk\s}% [\C]% [\C] \newphysicsconstant{Qproton}% {\ensuremath{Q_p}}% {+\echargevalue}% {\A\usk\s}% [\C]% [\C] \newphysicsconstant{qproton}% {\ensuremath{q_p}}% {+\echargevalue}% {\A\usk\s}% [\C]% [\C] \newphysicsconstant{MEarth}% {\ensuremath{M_{\text{Earth}}}}% {\mi@p{6.0}{5.97237}\timestento{24}}% {\kg}% [\kg]% [\kg] \newphysicsconstant{MMoon}% {\ensuremath{M_{\text{Moon}}}}% {\mi@p{7.3}{7.342}\timestento{22}}% {\kg}% [\kg]% [\kg] \newphysicsconstant{MSun}% {\ensuremath{M_{\text{Sun}}}}% {\mi@p{2.0}{1.98855}\timestento{30}}% {\kg}% [\kg]% [\kg] \newphysicsconstant{REarth}% {\ensuremath{R_{\text{Earth}}}}% {\mi@p{6.4}{6.371}\timestento{6}}% {\m}% [\m]% [\m] \newphysicsconstant{RMoon}% {\ensuremath{R_{\text{Moon}}}}% {\mi@p{1.7}{1.7371}\timestento{6}}% {\m}% [\m]% [\m] \newphysicsconstant{RSun}% {\ensuremath{R_{\text{Sun}}}}% {\mi@p{7.0}{6.957}\timestento{8}}% {\m}% [\m]% [\m] \newphysicsconstant{ESdist}% {\magvectsub{r}{ES}}% {\mi@p{1.5}{1.496}\timestento{11}}% {\m}% [\m]% [\m] \newphysicsconstant{SEdist}% {\magvectsub{r}{SE}}% {\mi@p{1.5}{1.496}\timestento{11}}% {\m}% [\m]% [\m] \newphysicsconstant{EMdist}% {\magvectsub{r}{EM}}% {\mi@p{3.8}{3.81550}\timestento{8}}% {\m}% [\m]% [\m] \newphysicsconstant{MEdist}% {\magvectsub{r}{ME}}% {\mi@p{3.8}{3.81550}\timestento{8}}% {\m}% [\m]% [\m] \newphysicsconstant{LSun}% {\ensuremath{L_{\text{Sun}}}}% {\mi@p{3.8}{3.8460}\timestento{26}}% {\m\squared\usk\kg\usk\s\reciprocalcubed}% [\W] [\J\per\s] \newphysicsconstant{TSun}% {\ensuremath{T_{\text{Sun}}}}% {\mi@p{5800}{5778}}% {\K}% [\K]% [\K] \newphysicsconstant{MagSun}% {\ensuremath{M_{\text{Sun}}}}% {+4.83}% {}% []% [] \newphysicsconstant{magSun}% {\ensuremath{m_{\text{Sun}}}}% {-26.74}% {}% []% [] \newcommand*{\coulombconstant}{\oofpez} \newcommand*{\altcoulombconstant}{\oofpezcs} \newcommand*{\biotsavartconstant}{\mzofp} \newcommand*{\boltzmannconstant}{\boltzmann} \newcommand*{\stefanboltzmannconstant}{\stefanboltzmann} \newcommand*{\planckconstant}{\planck} \newcommand*{\reducedplanckconstant}{\planckbar} \newcommand*{\planckconstanttimesc}{\planckc} \newcommand*{\rydbergconstant}{\rydberg} \newcommand*{\finestructureconstant}{\finestructure} \newcommand*{\avogadroconstant}{\avogadro} \newcommand*{\universalgravitationalconstant}{\universalgrav} \newcommand*{\earthssurfacegravitationalfield}{\surfacegravfield} \newcommand*{\photonconstant}{\clight} \newcommand*{\elementarycharge}{\echarge} \newcommand*{\EarthSundistance}{\ESdist} \newcommand*{\SunEarthdistance}{\SEdist} \newcommand*{\EarthMoondistance}{\ESdist} \newcommand*{\MoonEarthdistance}{\SEdist} \newcommand*{\Lstar}[1][\(\star\)]{\ensuremath{L_{\text{#1}}}\xspace} \newcommand*{\Lsolar}{\ensuremath{\Lstar[\(\odot\)]}\xspace} \newcommand*{\Tstar}[1][\(\star\)]{\ensuremath{T_{\text{#1}}}\xspace} \newcommand*{\Tsolar}{\ensuremath{\Tstar[\(\odot\)]}\xspace} \newcommand*{\Rstar}[1][\(\star\)]{\ensuremath{R_{\text{#1}}}\xspace} \newcommand*{\Rsolar}{\ensuremath{\Rstar[\(\odot\)]}\xspace} \newcommand*{\Mstar}[1][\(\star\)]{\ensuremath{M_{\text{#1}}}\xspace} \newcommand*{\Msolar}{\ensuremath{\Mstar[\(\odot\)]}\xspace} \newcommand*{\Fstar}[1][\(\star\)]{\ensuremath{F_{\text{#1}}}\xspace} \newcommand*{\fstar}[1][\(\star\)]{\ensuremath{f_{\text{#1}}}\xspace} \newcommand*{\Fsolar}{\ensuremath{\Fstar[\(\odot\)]}\xspace} \newcommand*{\fsolar}{\ensuremath{\fstar[\(\odot\)]}\xspace} \newcommand*{\Magstar}[1][\(\star\)]{\ensuremath{M_{\text{#1}}}\xspace} \newcommand*{\magstar}[1][\(\star\)]{\ensuremath{m_{\text{#1}}}\xspace} \newcommand*{\Magsolar}{\ensuremath{\Magstar[\(\odot\)]}\xspace} \newcommand*{\magsolar}{\ensuremath{\magstar[\(\odot\)]}\xspace} \newcommand*{\Dstar}[1][\(\star\)]{\ensuremath{D_{\text{#1}}}\xspace} \newcommand*{\dstar}[1][\(\star\)]{\ensuremath{d_{\text{#1}}}\xspace} \newcommand*{\Dsolar}{\ensuremath{\Dstar[\(\odot\)]}\xspace} \newcommand*{\dsolar}{\ensuremath{\dstar[\(\odot\)]}\xspace} \newcommand*{\onehalf}{\ensuremath{\frac{1}{2}}\xspace} \newcommand*{\onethird}{\ensuremath{\frac{1}{3}}\xspace} \newcommand*{\onefourth}{\ensuremath{\frac{1}{4}}\xspace} \newcommand*{\onefifth}{\ensuremath{\frac{1}{5}}\xspace} \newcommand*{\onesixth}{\ensuremath{\frac{1}{6}}\xspace} \newcommand*{\oneseventh}{\ensuremath{\frac{1}{7}}\xspace} \newcommand*{\oneeighth}{\ensuremath{\frac{1}{8}}\xspace} \newcommand*{\oneninth}{\ensuremath{\frac{1}{9}}\xspace} \newcommand*{\onetenth}{\ensuremath{\frac{1}{10}}\xspace} \newcommand*{\twooneths}{\ensuremath{\frac{2}{1}}\xspace} \newcommand*{\twohalves}{\ensuremath{\frac{2}{2}}\xspace} \newcommand*{\twothirds}{\ensuremath{\frac{2}{3}}\xspace} \newcommand*{\twofourths}{\ensuremath{\frac{2}{4}}\xspace} \newcommand*{\twofifths}{\ensuremath{\frac{2}{5}}\xspace} \newcommand*{\twosixths}{\ensuremath{\frac{2}{6}}\xspace} \newcommand*{\twosevenths}{\ensuremath{\frac{2}{7}}\xspace} \newcommand*{\twoeighths}{\ensuremath{\frac{2}{8}}\xspace} \newcommand*{\twoninths}{\ensuremath{\frac{2}{9}}\xspace} \newcommand*{\twotenths}{\ensuremath{\frac{2}{10}}\xspace} \newcommand*{\threeoneths}{\ensuremath{\frac{3}{1}}\xspace} \newcommand*{\threehalves}{\ensuremath{\frac{3}{2}}\xspace} \newcommand*{\threethirds}{\ensuremath{\frac{3}{3}}\xspace} \newcommand*{\threefourths}{\ensuremath{\frac{3}{4}}\xspace} \newcommand*{\threefifths}{\ensuremath{\frac{3}{5}}\xspace} \newcommand*{\threesixths}{\ensuremath{\frac{3}{6}}\xspace} \newcommand*{\threesevenths}{\ensuremath{\frac{3}{7}}\xspace} \newcommand*{\threeeighths}{\ensuremath{\frac{3}{8}}\xspace} \newcommand*{\threeninths}{\ensuremath{\frac{3}{9}}\xspace} \newcommand*{\threetenths}{\ensuremath{\frac{3}{10}}\xspace} \newcommand*{\fouroneths}{\ensuremath{\frac{4}{1}}\xspace} \newcommand*{\fourhalves}{\ensuremath{\frac{4}{2}}\xspace} \newcommand*{\fourthirds}{\ensuremath{\frac{4}{3}}\xspace} \newcommand*{\fourfourths}{\ensuremath{\frac{4}{4}}\xspace} \newcommand*{\fourfifths}{\ensuremath{\frac{4}{5}}\xspace} \newcommand*{\foursixths}{\ensuremath{\frac{4}{6}}\xspace} \newcommand*{\foursevenths}{\ensuremath{\frac{4}{7}}\xspace} \newcommand*{\foureighths}{\ensuremath{\frac{4}{8}}\xspace} \newcommand*{\fourninths}{\ensuremath{\frac{4}{9}}\xspace} \newcommand*{\fourtenths}{\ensuremath{\frac{4}{10}}\xspace} \newcommand*{\sumoverall}[1]{\ensuremath{\displaystyle \sum_{\substack{\text{\tiny{all }}\text{\tiny{{#1}}}}}}} \newcommand*{\dx}[1]{\ensuremath{\,\mathrm{d}{#1}}} \newcommand*{\dslashx}[1]{\ensuremath{\,\mathchar'26\mkern-12mu \mathrm{d}{#1}}} \newcommandx{\evaluatedfromto}[2][2,usedefault]{\ensuremath{% \Bigg.\Bigg\rvert_{#1}^{#2}}} \newcommand*{\evaluatedat}{\evaluatedfromto} \newcommandx{\integral}[4][1,2,usedefault]{\ensuremath{% \int_{\ifthenelse{\equal{#1}{}}{}{#4=#1}}^{\ifthenelse{% \equal{#2}{}}{}{#4=#2}}}{#3}\dx{#4}} \newcommand*{\opensurfaceintegral}[2]{\ensuremath{% \iint\nolimits_{#1}\vectdotvect{#2}{\dirvect{n}}\dx{A}}} \newcommand*{\closedsurfaceintegral}[2]{\ensuremath{% \varoiint\nolimits_{#1}\vectdotvect{#2}{\dirvect{n}}\dx{A}}} \newcommand*{\openlineintegral}[2]{\ensuremath{% \int\nolimits_{#1}\vectdotvect{#2}{\dirvect{t}}\dx{\ell}}} \newcommand*{\closedlineintegral}[2]{\ensuremath{% \oint\nolimits_{#1}\vectdotvect{#2}{\dirvect{t}}\dx{\ell}}} \newcommand*{\volumeintegral}[2]{\ensuremath{% \iiint\nolimits_{#1}{#2}\dx{V}}} \newcommandx{\dbydt}[1][1]{\ensuremath{% \frac{\mathrm{d}{#1}}{\mathrm{d}t}}} \newcommandx{\DbyDt}[1][1]{\ensuremath{% \frac{\Delta{#1}}{\Delta t}}} \newcommandx{\ddbydt}[1][1]{\ensuremath{% \frac{\mathrm{d}^{2}{#1}}{\mathrm{d}t^{2}}}} \newcommandx{\DDbyDt}[1][1]{\ensuremath{% \frac{\Delta^{2}{#1}}{\Delta t^{2}}}} \newcommandx{\pbypt}[1][1]{\ensuremath{% \frac{\partial{#1}}{\partial t}}} \newcommandx{\ppbypt}[1][1]{\ensuremath{% \frac{\partial^{2}{#1}}{\partial t^{2}}}} \newcommand*{\dbyd}[2]{\ensuremath{\frac{% \mathrm{d}{#1}}{\mathrm{d}{#2}}}} \newcommand*{\DbyD}[2]{\ensuremath{\frac{% \Delta{#1}}{\Delta{#2}}}} \newcommand*{\ddbyd}[2]{\ensuremath{% \frac{\mathrm{d}^{2}{#1}}{\mathrm{d}{#2}^{2}}}} \newcommand*{\DDbyD}[2]{\ensuremath{% \frac{\Delta^{2}{#1}}{\Delta{#2}^{2}}}} \newcommand*{\pbyp}[2]{\ensuremath{% \frac{\partial{#1}}{\partial{#2}}}} \newcommand*{\ppbyp}[2]{\ensuremath{% \frac{\partial^{2}{#1}}{\partial{#2}^{2}}}} \newcommandx{\seriesfofx}[1][1=x,usedefault]{\ensuremath{% f({#1}) \approx f(a) + \frac{f^\prime (a)}{1!}({#1}-a) + \frac{f^{\prime\prime}(a)}{2!}({#1}-a)^2 + \frac{f^{\prime\prime\prime}(a)}{3!}({#1}-a)^3 + \ldots}\xspace} \newcommandx{\seriesexpx}[1][1=x,usedefault]{\ensuremath{% e^{#1} \approx 1 + {#1} + \frac{{#1}^2}{2!} + \frac{{#1}^3}{3!} + \ldots}\xspace} \newcommandx{\seriessinx}[1][1=x,usedefault]{\ensuremath{% \sin {#1} \approx {#1} - \frac{{#1}^3}{3!} + \frac{{#1}^5}{5!} - \ldots}\xspace} \newcommandx{\seriescosx}[1][1=x,usedefault]{\ensuremath{% \cos {#1} \approx 1 - \frac{{#1}^2}{2!} + \frac{{#1}^4}{4!} - \ldots}\xspace} \newcommandx{\seriestanx}[1][1=x,usedefault]{\ensuremath{% \tan {#1} \approx {#1} + \frac{{#1}^3}{3} + \frac{2{#1}^5}{15} + \ldots}\xspace} \newcommandx{\seriesatox}[1][1=x,usedefault]{\ensuremath{% a^{#1} \approx 1 + {#1} \ln{a} + \frac{({#1} \ln a)^2}{2!} + \frac{({#1} \ln a)^3}{3!} + \ldots}\xspace} \newcommandx{\serieslnoneplusx}[1][1=x,usedefault]{\ensuremath{% \ln(1 \pm {#1}) \approx \pm\; {#1} - \frac{{#1}^2}{2} \pm \frac{{#1}^3}{3} - % \frac{{#1}^4}{4} \pm \ldots}\xspace} \newcommandx{\binomialseries}[1][1=x,usedefault]{\ensuremath{% (1 + {#1})^n \approx 1 + n{#1} + \frac{n(n-1)}{2!}{#1}^2 + \ldots}\xspace} \newcommand*{\gradient}{\ensuremath{\boldsymbol{\nabla}}} \newcommand*{\divergence}{\ensuremath{\boldsymbol{\nabla}\bullet}} \newcommand*{\curl}{\ensuremath{\boldsymbol{\nabla\times}}} \newcommand{\taigrad}{\ensuremath{\nabla}}% \newcommand{\taisvec}{\ensuremath{% \stackinset{c}{0.07ex}{c}{0.1ex}{\tiny$-$}{$\nabla$}} }% \newcommand{\taidivg}{\ensuremath{% \stackinset{c}{0.07ex}{c}{0.1ex}{$\cdot$}{$\nabla$}} }% \newcommand{\taicurl}{\ensuremath{% \stackinset{c}{0.04ex}{c}{0.32ex}{\tiny$\times$}{$\nabla$}} }% \newcommand*{\laplacian}{\ensuremath{\boldsymbol{\nabla}^2}} \newcommand*{\dalembertian}{\ensuremath{\boldsymbol{\Box}}} \newcommand*{\diracdelta}[1]{\ensuremath{\delta}(#1)} \newcommand*{\orderof}[1]{\ensuremath{\mathcal{O}(#1)}} \DeclareMathOperator{\asin}{\sin^{-1}} 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\ifthenelse{\equal{#2}{}} {\unit{10^{#1}}{}} {\unit{10^{#1}}{#2}}}} \newcommand*{\ee}[2]{\texttt{{#1}e{#2}}} \newcommand*{\EE}[2]{\texttt{{#1}E{#2}}} \newcommand*{\dms}[3]{\ensuremath{% \indegrees{#1}\inarcminutes{#2}\inarcseconds{#3}}} \newcommand*{\hms}[3]{\ensuremath{% {#1}^{\hour}{#2}^{\mathrm{m}}{#3}^{\s}}} \newcommand*{\clockreading}{\hms} \newcommand*{\latitude}[1]{\unit{#1}{\mkern-\thickmuskip\degree}} \newcommand*{\latitudeN}[1]{\unit{#1}{\mkern-\thickmuskip\degree\;\mathrm{N}}} \newcommand*{\latitudeS}[1]{\unit{#1}{\mkern-\thickmuskip\degree\;\mathrm{S}}} \newcommand*{\longitude}[1]{\unit{#1}{\mkern-\thickmuskip\degree}} \newcommand*{\longitudeE}[1]{\unit{#1}{\mkern-\thickmuskip\degree\;\mathrm{E}}} \newcommand*{\longitudeW}[1]{\unit{#1}{\mkern-\thickmuskip\degree\;\mathrm{W}}} \newcommand*{\ssub}[2]{\ensuremath{#1_{\text{#2}}}} \newcommand*{\ssup}[2]{\ensuremath{#1^{\text{#2}}}} \newcommand*{\ssud}[3]{\ensuremath{#1^{\text{#2}}_{\text{#3}}}} 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\newcommand*{\cuberoot}[1]{\ensuremath{\sqrt[3]{#1}}} \newcommand*{\fourthroot}[1]{\ensuremath{\sqrt[4]{#1}}} \newcommand*{\fifthroot}[1]{\ensuremath{\sqrt[5]{#1}}} \newcommand*{\fsqrt}[1]{\ensuremath{{#1}^\onehalf}} \newcommand*{\fcuberoot}[1]{\ensuremath{{#1}^\onethird}} \newcommand*{\ffourthroot}[1]{\ensuremath{{#1}^\onefourth}} \newcommand*{\ffifthroot}[1]{\ensuremath{{#1}^\onefifth}} \newcommand*{\relgamma}[1]{\ensuremath{% \frac{1}{\sqrt{1-\inparens{\frac{#1}{c}}\squared}}}} \newcommand*{\frelgamma}[1]{\ensuremath{% \inparens{1-\frac{{#1}\squared}{c\squared}}^{-\onehalf}}} \newcommand*{\oosqrtomxs}[1]{\ensuremath{\frac{1}{\sqrt{1-{#1}\squared}}}} \newcommand*{\oosqrtomx}[1]{\ensuremath{\frac{1}{\sqrt{1-{#1}}}}} \newcommand*{\ooomx}[1]{\ensuremath{\frac{1}{1-{#1}}}} \newcommand*{\ooopx}[1]{\ensuremath{\frac{1}{1+{#1}}}} \newcommand*{\isequals}{\wordoperator{?}{=}\xspace} \newcommand*{\wordoperator}[2]{\ensuremath{% \mathrel{\vcenter{\offinterlineskip \halign{\hfil\tiny\upshape##\hfil\cr\noalign{\vskip-.5ex} {#1}\cr\noalign{\vskip.5ex}{#2}\cr}}}}} \newcommand*{\definedas}{\wordoperator{defined}{as}\xspace} \newcommand*{\associated}{\wordoperator{associated}{with}\xspace} \newcommand*{\adjustedby}{\wordoperator{adjusted}{by}\xspace} \newcommand*{\earlierthan}{\wordoperator{earlier}{than}\xspace} \newcommand*{\laterthan}{\wordoperator{later}{than}\xspace} \newcommand*{\forevery}{\wordoperator{for}{every}\xspace} \newcommand*{\pwordoperator}[2]{\ensuremath{\left(% \mathrel{\vcenter{\offinterlineskip% \halign{\hfil\tiny\upshape##\hfil\cr\noalign{\vskip-.5ex}% {#1}\cr\noalign{\vskip.5ex}{#2}\cr}}}\right)}}% \newcommand*{\pdefinedas}{\pwordoperator{defined}{as}\xspace} \newcommand*{\passociated}{\pwordoperator{associated}{with}\xspace} \newcommand*{\padjustedby}{\pwordoperator{adjusted}{by}\xspace} \newcommand*{\pearlierthan}{\pwordoperator{earlier}{than}\xspace} \newcommand*{\platerthan}{\pwordoperator{later}{than}\xspace} \newcommand*{\pforevery}{\pwordoperator{for}{every}\xspace} \newcommand*{\defines}{\ensuremath{\stackrel{\text{\tiny{def}}}{=}}\xspace} \newcommand*{\inframe}[1][\relax]{\ensuremath{% \xrightarrow[\text\tiny{\mathcal #1}]{}}\xspace} \newcommand*{\associates}{\ensuremath{% \xrightarrow{\text{\tiny{assoc}}}}\xspace} \newcommand*{\becomes}{\ensuremath{% \xrightarrow{\text{\tiny{becomes}}}}\xspace} \newcommand*{\rrelatedto}[1]{\ensuremath{% \xLongrightarrow{\text{\tiny{#1}}}}} \newcommand*{\lrelatedto}[1]{\ensuremath{% \xLongleftarrow[\text{\tiny{#1}}]{}}} \newcommand*{\brelatedto}[2]{\ensuremath{% \xLongleftrightarrow[\text{\tiny{#1}}]{\text{\tiny{#2}}}}} \newcommand*{\genericinteractionplaces}[5]{\ensuremath{\inparens{#1} \frac{\inparens{#2}\inparens{#3}}{\inparens{#4}^2}{{\ifblank{#5}{% \mivector{\_ , \_ , \_}}{#5}}}}} \newcommand*{\genericfieldofparticleplaces}[4]{\ensuremath{\inparens{#1} \frac{\inparens{#2}}{\inparens{#3}^2}{{\ifblank{#4}{\mivector{\_ , \_ , \_}}{#4}}}}} \newcommand*{\genericpotentialenergyplaces}[4]{\ensuremath{% \inparens{#1}\frac{\inparens{#2}\inparens{#3}}{\inparens{#4}}}} \newcommand*{\genericelectricdipoleplaces}[5]{% \ensuremath{\inparens{#1}\frac{\inparens{#2}\inparens{#3}}{\inparens{#4}^3}% {{\ifblank{#5}{\mivector{\_ , \_ , \_}}{#5}}}}} \newcommand*{\genericelectricdipoleonaxisplaces}[5]{% \ensuremath{\inparens{#1}\frac{2\inparens{#2}\inparens{#3}}{\inparens{#4}^3}% {{\ifblank{#5}{\mivector{\_ , \_ , \_}}{#5}}}}} \newcommand*{\gfieldofparticle}{\ensuremath{\universalgravmathsymbol\frac{M}% {\magsquaredvect{r}}\inparens{-\dirvect{r}}}} \newcommand*{\gravitationalinteractionplaces}[4]{% \genericinteractionplaces{\universalgrav}{#1}{#2}{#3}{#4}} \newcommand*{\gfieldofparticleplaces}[3]{% \genericfieldofparticleplaces{\universalgrav}{#1}{#2}{#3}} \newcommand*{\electricinteractionplaces}[4]{% \genericinteractionplaces{\oofpez}{#1}{#2}{#3}{#4}} \newcommand*{\Efieldofparticleplaces}[3]{% \genericfieldofparticleplaces{\oofpez}{#1}{#2}{#3}} \newcommand*{\Bfieldofparticleplaces}[5]{\ensuremath{\inparens{\mzofp}% \frac{\inparens{#1}\inparens{#2}}{\inparens{#3}^2}{{\ifblank{#4}{% \mivector{\_ , \_ , \_}}{#4}}}\times{{\ifblank{#5}{\mivector{\_ , \_ , \_}}{#5}}}}} \newcommand*{\springinteractionplaces}[3]{\ensuremath{\inparens{#1} \inparens{#2}{{\ifblank{#3}{\mivector{\_ , \_ , \_}}{#3}}}}} \newcommand*{\gravitationalpotentialenergyplaces}[3]{\ensuremath{% -\genericpotentialenergyplaces{\universalgrav}{#1}{#2}{#3}}} \newcommand*{\electricpotentialenergyplaces}[3]{% \genericpotentialenergyplaces{\oofpez}{#1}{#2}{#3}} \newcommand*{\springpotentialenergyplaces}[2]{\ensuremath{% \onehalf\inparens{#1}\inparens{#2}^2}} \newcommand*{\electricdipoleonaxisplaces}[4]{% \genericelectricdipoleonaxisplaces{\oofpez}{\absof{#1}}{#2}{#3}{{\ifblank{#4}{% \mivector{\_ , \_ , \_}}{#4}}}} \newcommand*{\electricdipoleonbisectorplaces}[4]{% \genericelectricdipoleplaces{\oofpez}{\absof{#1}}{#2}{#3}{{\ifblank{#4}{% \mivector{\_ , \_ , \_}}{#4}}}} \newcommand{\define}[2]{\newcommand{#1}{#2}} \newcommand*{\momentumprinciple}{\ensuremath{% \vectsub{p}{sys,final}=\vectsub{p}{sys,initial}+\Fnetsys\Delta t}} \newcommand*{\LHSmomentumprinciple}{\ensuremath{\vectsub{p}{sys,final}}} \newcommand*{\RHSmomentumprinciple}{\ensuremath{% \vectsub{p}{sys,initial}+\Fnetsys\Delta t}} \newcommand*{\momentumprinciplediff}{\ensuremath{% \Dvectsub{p}{sys}=\Fnetsys\Delta t}} \newcommand*{\energyprinciple}{\ensuremath{% \ssub{E}{sys,final}=\ssub{E}{sys,initial}+W+Q}} \newcommand*{\LHSenergyprinciple}{\ensuremath{\ssub{E}{sys,final}}} \newcommand*{\RHSenergyprinciple}{\ensuremath{\ssub{E}{sys,initial}+W+Q}} \newcommand*{\energyprinciplediff}{\ensuremath{\Delta\ssub{E}{sys}=W+Q}} \newcommand*{\angularmomentumprinciple}{\ensuremath{% \vectsub{L}{\(A\),sys,final}=\vectsub{L}{\(A\),sys,initial}+\Tsub{net}\Delta t}} \newcommand*{\LHSangularmomentumprinciple}{\ensuremath{% \vectsub{L}{\(A\),sys,final}}} \newcommand*{\RHSangularmomentumprinciple}{\ensuremath{% \vectsub{L}{\(A\),sys,initial}+\Tsub{net}\Delta t}} \newcommand*{\angularmomentumprinciplediff}{\ensuremath{% \Dvectsub{L}{\(A\),sys}=\Tsub{net}\Delta t}} \newcommand*{\gravitationalinteraction}{\ensuremath{% \universalgravmathsymbol\frac{\msub{M}{1}\msub{M}{2}}{% \magvectsub{r}{12}\squared}(-\dirvectsub{r}{12})}} \newcommand*{\electricinteraction}{\ensuremath{% \oofpezmathsymbol\frac{\msub{Q}{1}\msub{Q}{2}}{\magvectsub{r}{12}\squared} \dirvectsub{r}{12}}} \newcommand*{\springinteraction}{\ensuremath{\ks\magvect{s}(-\dirvect{s})}} \newcommand*{\Bfieldofparticle}{\ensuremath{% \mzofpmathsymbol\frac{Q\magvect{v}}{\magsquaredvect{r}}\dirvect{v}\times \dirvect{r}}} \newcommand*{\Efieldofparticle}{\ensuremath{% \oofpezmathsymbol\frac{Q}{\magsquaredvect{r}}\dirvect{r}}} \newcommandx{\Esys}[1][1]{\ifthenelse{% \equal{#1}{}}{\ssub{E}{sys}}{\ssub{E}{sys,#1}}} \newcommandx{\Us}[1][1]{\ifthenelse{% \equal{#1}{}}{\ssub{U}{\(s\)}}{\ssub{U}{\(s\),#1}}} \newcommandx{\Ug}[1][1]{\ifthenelse{% \equal{#1}{}}{\ssub{U}{\(g\)}}{\ssub{U}{\(g\),#1}}} \newcommandx{\Ue}[1][1]{\ifthenelse{% \equal{#1}{}}{\ssub{U}{\(e\)}}{\ssub{U}{\(e\),#1}}} \newcommandx{\Ktrans}[1][1]{\ifthenelse{\equal{#1}{}}{\ssub{K}{trans}} {\ssub{K}{trans,#1}}} \newcommandx{\Krot}[1][1]{\ifthenelse{% \equal{#1}{}}{\ssub{K}{rot}}{\ssub{K}{rot,#1}}} \newcommandx{\Kvib}[1][1]{\ifthenelse{% \equal{#1}{}}{\ssub{K}{vib}}{\ssub{K}{vib,#1}}} \newcommandx{\Eparticle}[1][1]{\ifthenelse{\equal{#1}{}}{\ssub{E}{particle}} {\ssub{E}{particle,#1}}} \newcommandx{\Einternal}[1][1]{\ifthenelse{\equal{#1}{}}{\ssub{E}{internal}} {\ssub{E}{internal,#1}}} \newcommandx{\Erest}[1][1]{\ifthenelse{\equal{#1}{}}{\ssub{E}{rest}}{\ssub{E} {rest,#1}}} \newcommandx{\Echem}[1][1]{\ifthenelse{\equal{#1}{}}{\ssub{E}{chem}}{\ssub{E} {chem,#1}}} \newcommandx{\Etherm}[1][1]{\ifthenelse{\equal{#1}{}}{\ssub{E}{therm}} {\ssub{E}{therm,#1}}} \newcommandx{\Evib}[1][1]{\ifthenelse{% \equal{#1}{}}{\ssub{E}{vib}}{\ssub{E}{vib,#1}}} \newcommandx{\Ephoton}[1][1]{\ifthenelse{\equal{#1}{}}{\ssub{E}{photon}} {\ssub{E}{photon,#1}}} \newcommand*{\DEsys}{\Changein\Esys} \newcommand*{\DUs}{\Changein\Us} \newcommand*{\DUg}{\Changein\Ug} \newcommand*{\DUe}{\Changein\Ue} \newcommand*{\DKtrans}{\Changein\Ktrans} \newcommand*{\DKrot}{\Changein\Krot} \newcommand*{\DKvib}{\Changein\Kvib} \newcommand*{\DEparticle}{\Changein\Eparticle} \newcommand*{\DEinternal}{\Changein\Einternal} \newcommand*{\DErest}{\Changein\Erest} \newcommand*{\DEchem}{\Changein\Echem} \newcommand*{\DEtherm}{\Changein\Etherm} \newcommand*{\DEvib}{\Changein\Evib} \newcommand*{\DEphoton}{\Changein\Ephoton} \newcommand*{\springpotentialenergy}{\onehalf\ks\magsquaredvect{s}} \newcommand*{\finalspringpotentialenergy} {\ssub{\left(\springpotentialenergy\right)}{\!\!final}} \newcommand*{\initialspringpotentialenergy} {\ssub{\left(\springpotentialenergy\right)}{\!\!initial}} \newcommand*{\gravitationalpotentialenergy}{\ensuremath{% -G\frac{\msub{M}{1}\msub{M}{2}}{\magvectsub{r}{12}}}} \newcommand*{\finalgravitationalpotentialenergy} {\ssub{\left(\gravitationalpotentialenergy\right)}{\!\!final}} \newcommand*{\initialgravitationalpotentialenergy} {\ssub{\left(\gravitationalpotentialenergy\right)}{\!\!initial}} \newcommand*{\electricpotentialenergy}{\ensuremath{% \oofpezmathsymbol\frac{\ssub{Q}{1}\ssub{Q}{2}}{\magvectsub{r}{12}}}} \newcommand*{\finalelectricpotentialenergy} {\ssub{\left(\electricpotentialenergy\right)}{\!\!final}} \newcommand*{\initialelectricpotentialenergy} {\ssub{\left(\electricpotentialenergy\right)}{\!\!initial}} \newcommand*{\ks}{\msub{k}{s}} \newcommand*{\Fnet}{\ensuremath{\vectsub{F}{net}}} \newcommand*{\Fnetext}{\ensuremath{\vectsub{F}{net,ext}}} \newcommand*{\Fnetsys}{\ensuremath{\vectsub{F}{net,sys}}} \newcommand*{\Fsub}[1]{\ensuremath{\vectsub{F}{#1}}} \newcommand*{\Ltotal}{\ensuremath{\vectsub{L}{\(A\),total}}} \newcommand*{\Lsys}{\ensuremath{\vectsub{L}{\(A\),sys}}} \newcommand*{\Lsub}[1]{\ensuremath{\vectsub{L}{\(A\),{#1}}}} \newcommand*{\Tnet}{\ensuremath{\vectsub{\tau}{\(A\),net}}} \newcommand*{\Tnetext}{\ensuremath{\vectsub{\tau}{\(A\),net,ext}}} \newcommand*{\Tnetsys}{\ensuremath{\vectsub{\tau}{\(A\),net,sys}}} \newcommand*{\Tsub}[1]{\ensuremath{\vectsub{\tau}{\(A\),#1}}} \newcommand*{\LHSmaxwelliint}[1][\partial V]{\ensuremath{% \closedsurfaceintegral{#1}{\vect{E}}}} \newcommand*{\RHSmaxwelliint}{\ensuremath{\frac{\ssub{Q}{\(e\),net}}% {\vacuumpermittivitymathsymbol}}} \newcommand*{\RHSmaxwelliinta}[1][V]{\ensuremath{% \frac{1}{\vacuumpermittivitymathsymbol}\volumeintegral{#1}{\msub{\rho}{e}}}} \newcommand*{\RHSmaxwelliintfree}{\ensuremath{0}} \newcommand*{\maxwelliint}[1][\partial V]{\ensuremath{% \LHSmaxwelliint[#1]=\RHSmaxwelliint}} \newcommandx*{\maxwelliinta}[2][1={\partial V},2={V},usedefault]{\ensuremath{% \LHSmaxwelliint[#1]=\RHSmaxwelliinta[#2]}} \newcommand*{\maxwelliintfree}[1][\partial V]{\ensuremath{% \LHSmaxwelliint[#1]=\RHSmaxwelliintfree}} \newcommand*{\LHSmaxwelliiint}[1][\partial V]{\ensuremath{% \closedsurfaceintegral{#1}{\vect{B}}}} \newcommand*{\RHSmaxwelliiint}{\ensuremath{0}} \newcommand*{\RHSmaxwelliiintm}{\ensuremath{% \vacuumpermeabilitymathsymbol\ssub{Q}{\(m\),net}}} \newcommand*{\RHSmaxwelliiintma}[1][V]{\ensuremath{% \vacuumpermeabilitymathsymbol\volumeintegral{#1}{\msub{\rho}{m}}}} \newcommand*{\RHSmaxwelliiintfree}{\ensuremath{0}} \newcommand*{\maxwelliiint}[1][\partial V]{\ensuremath{% \LHSmaxwelliiint[#1]=\RHSmaxwelliiint}} \newcommand*{\maxwelliiintm}[1][\partial V]{\ensuremath{% \LHSmaxwelliiint[#1]=\RHSmaxwelliiintm}} \newcommandx*{\maxwelliiintma}[2][1={\partial V},2={V},usedefault]{\ensuremath{% \LHSmaxwelliiint[#1]=\RHSmaxwelliiintma[#2]}} \newcommand*{\maxwelliiintfree}[1][\partial V]{\ensuremath{% \LHSmaxwelliiint[#1]=\RHSmaxwelliiintfree}} \newcommand*{\LHSmaxwelliiiint}[1][\partial\Omega]{\ensuremath{% \closedlineintegral{#1}{\vect{E}}}} \newcommand*{\RHSmaxwelliiiint}[1][\Omega]{\ensuremath{% -\dbydt\opensurfaceintegral{#1}{\vect{B}}}} \newcommand*{\RHSmaxwelliiiintm}[1][\Omega]{\ensuremath{% -\dbydt\opensurfaceintegral{#1}{\vect{B}}% -\vacuumpermeabilitymathsymbol\ssub{I}{\(m\),net}}} \newcommand*{\RHSmaxwelliiiintma}[1][\Omega]{\ensuremath{% -\dbydt\opensurfaceintegral{#1}{\vect{B}}% -\vacuumpermeabilitymathsymbol\opensurfaceintegral{#1}{\vectsub{J}{\(m\)}}}} \newcommand*{\RHSmaxwelliiiintfree}{\RHSmaxwelliiiint} \newcommandx*{\maxwelliiiint}[2][1={\partial\Omega},2={\Omega},usedefault]% {\ensuremath{\LHSmaxwelliiiint[#1]=\RHSmaxwelliiiint[#2]}} \newcommandx*{\maxwelliiiintm}[2][1={\partial\Omega},2={\Omega},usedefault]% {\ensuremath{\LHSmaxwelliiiint[#1]=\RHSmaxwelliiiintm[#2]}} \newcommandx*{\maxwelliiiintma}[2][1={\partial\Omega},2={\Omega},usedefault]% {\ensuremath{\LHSmaxwelliiiint[#1]=\RHSmaxwelliiiintma[#2]}} \newcommand*{\maxwelliiiintfree}{\maxwelliiiint} \newcommand*{\LHSmaxwellivint}[1][\partial\Omega]{\ensuremath{% \closedlineintegral{#1}{\vect{B}}}} \newcommand*{\RHSmaxwellivint}[1][\Omega]{\ensuremath{% \vacuumpermeabilitymathsymbol\vacuumpermittivitymathsymbol% \dbydt\opensurfaceintegral{#1}{\vect{E}}+% \vacuumpermeabilitymathsymbol\ssub{I}{\(e\),net}}} \newcommand*{\RHSmaxwellivinta}[1][\Omega]{\ensuremath{% \vacuumpermeabilitymathsymbol\vacuumpermittivitymathsymbol% \dbydt\opensurfaceintegral{#1}{\vect{E}}+% \vacuumpermeabilitymathsymbol\opensurfaceintegral{#1}{\vectsub{J}{\(e\)}}}} \newcommand*{\RHSmaxwellivintfree}[1][\Omega]{\ensuremath{% \vacuumpermeabilitymathsymbol\vacuumpermittivitymathsymbol% \dbydt\opensurfaceintegral{#1}{\vect{E}}}} \newcommandx*{\maxwellivint}[2][1={\partial\Omega},2={\Omega},usedefault]% {\ensuremath{\LHSmaxwellivint[#1]=\RHSmaxwellivint[#2]}} \newcommandx*{\maxwellivinta}[2][1={\partial\Omega},2={\Omega},usedefault]% {\ensuremath{\LHSmaxwellivint[#1]=\RHSmaxwellivinta[#2]}} \newcommandx*{\maxwellivintfree}[2][1={\partial\Omega},2={\Omega},usedefault]% {\ensuremath{\LHSmaxwellivint[#1]=\RHSmaxwellivintfree[#2]}} \newcommand*{\LHSmaxwellidif}{\ensuremath{\divergence{\vect{E}}}} \newcommand*{\RHSmaxwellidif}{\ensuremath{\frac{\msub{\rho}{e}} {\vacuumpermittivitymathsymbol}}} \newcommand*{\RHSmaxwellidiffree}{\ensuremath{0}} \newcommand*{\maxwellidif}{\ensuremath{\LHSmaxwellidif=\RHSmaxwellidif}} \newcommand*{\maxwellidiffree}{\ensuremath{\LHSmaxwellidif=\RHSmaxwellidiffree}} \newcommand*{\LHSmaxwelliidif}{\ensuremath{\divergence{\vect{B}}}} \newcommand*{\RHSmaxwelliidif}{\ensuremath{0}} \newcommand*{\RHSmaxwelliidifm}{\ensuremath{\vacuumpermeabilitymathsymbol% \msub{\rho}{m}}} \newcommand*{\RHSmaxwelliidiffree}{\ensuremath{0}} \newcommand*{\maxwelliidif}{\ensuremath{\LHSmaxwelliidif=\RHSmaxwelliidif}} \newcommand*{\maxwelliidifm}{\ensuremath{\LHSmaxwelliidif=\RHSmaxwelliidifm}} \newcommand*{\maxwelliidiffree}{\ensuremath{\LHSmaxwelliidif=\RHSmaxwelliidiffree}} \newcommand*{\LHSmaxwelliiidif}{\ensuremath{\curl{\vect{E}}}} \newcommand*{\RHSmaxwelliiidif}{\ensuremath{-\pbypt[\vect{B}]}} \newcommand*{\RHSmaxwelliiidifm}{\ensuremath{-\pbypt[\vect{B}]-% \vacuumpermeabilitymathsymbol\vectsub{J}{\(m\)}}} \newcommand*{\RHSmaxwelliiidiffree}{\RHSmaxwelliiidif} \newcommand*{\maxwelliiidif}{\ensuremath{\LHSmaxwelliiidif=\RHSmaxwelliiidif}} \newcommand*{\maxwelliiidifm}{\ensuremath{\LHSmaxwelliiidif=\RHSmaxwelliiidifm}} \newcommand*{\maxwelliiidiffree}{\ensuremath{\LHSmaxwelliiidif=\RHSmaxwelliiidif}} \newcommand*{\LHSmaxwellivdif}{\ensuremath{\curl{\vect{B}}}} \newcommand*{\RHSmaxwellivdif}{\ensuremath{\vacuumpermeabilitymathsymbol% \vacuumpermittivitymathsymbol\pbypt[\vect{E}]+% \vacuumpermeabilitymathsymbol\vectsub{J}{\(e\)}}} \newcommand*{\RHSmaxwellivdiffree}{\ensuremath{\vacuumpermeabilitymathsymbol \vacuumpermittivitymathsymbol\pbypt[\vect{E}]}} \newcommand*{\maxwellivdif}{\ensuremath{\LHSmaxwellivdif=\RHSmaxwellivdif}} \newcommand*{\maxwellivdiffree}{\ensuremath{\LHSmaxwellivdif=\RHSmaxwellivdiffree}} \newcommand*{\RHSlorentzforce}{\ensuremath{\msub{q}{e}\left(\vect{E}+% \vectcrossvect{\vect{v}}{\vect{B}}\right)}} \newcommand*{\RHSlorentzforcem}{\ensuremath{\RHSlorentzforce+\msub{q}{m}\left(% \vect{B}-\vectcrossvect{\vect{v}}{\frac{\vect{E}}{c^2}}\right)}} \newcommandx{\eulerlagrange}[1][1={q_i},usedefault]{\ensuremath{% \pbyp{\mathcal{L}}{#1}-\dbydt\inparens{\pbyp{\mathcal{L}}{\dot{#1}}} = 0}} \newcommandx{\Eulerlagrange}[1][1={q_i},usedefault]{\ensuremath{% \DbyD{\mathcal{L}}{#1}-\DbyDt\inparens{\DbyD{\mathcal{L}}{\dot{#1}}} = 0}} \newcommand*{\vpythonline}{\lstinline[style=vpython]} \newcommand*{\glowscriptline}{\lstinline[style=vpython]} 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hidealllines=false,skipbelow=\baselineskip,skipabove=\baselineskip, leftmargin=40pt,rightmargin=40pt,linewidth=1,roundcorner=10, nobreak=true, frametitle={INSTRUCTOR NOTE}, frametitlebackgroundcolor=gray!50,frametitlerule=true,frametitlerulewidth=1, backgroundcolor=gray!20, linecolor=black,fontcolor=black,shadow=true} \NewEnviron{bwinstructornote}{% \begin{mdframed}[style=bwinstructornotestyle] \begin{adjactivityanswer}[gray!20][gray!20][black] \BODY \end{adjactivityanswer} \end{mdframed} }% \mdfdefinestyle{bwstudentnotestyle}{% hidealllines=false,skipbelow=\baselineskip,skipabove=\baselineskip, leftmargin=40pt,rightmargin=40pt,linewidth=1,roundcorner=10, nobreak=true, frametitle={STUDENT NOTE}, frametitlebackgroundcolor=gray!50,frametitlerule=true,frametitlerulewidth=1, backgroundcolor=gray!20, linecolor=black,fontcolor=black,shadow=true} \NewEnviron{bwstudentnote}{% \begin{mdframed}[style=bwstudentnotestyle] \begin{adjactivityanswer}[gray!20][gray!20][black] \BODY 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