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diff --git a/Master/texmf-dist/tex/latex/mecaso/mecaso.sty b/Master/texmf-dist/tex/latex/mecaso/mecaso.sty new file mode 100644 index 00000000000..dd2f5c2bb46 --- /dev/null +++ b/Master/texmf-dist/tex/latex/mecaso/mecaso.sty @@ -0,0 +1,281 @@ +%Mecaso, un package LaTeX pour les formules en mécanique du solide +%Conçu par : Youssef DERRAZI, version 1.0 +%Distribué sous la license GNU Public License V3.0 + +\NeedsTeXFormat{LaTeX2e} +\ProvidesPackage{mecaso}[2021/08/27 v1.0] + +\RequirePackage{amsmath} +\RequirePackage{amssymb} +\RequirePackage{mathrsfs} + +%Commands : +\newcommand{\R}{\mathbb{R}} + +%Derivative on line \Dex[R]{u(t)} : +\newcommand{\Dex}[2][R]{\frac{d}{dt}{#2}\bigg|_{#1}} + +%Derivative on fraction \Din[R]{u(t)} : +\newcommand{\Din}[2][R]{\frac{d{#2}}{dt}\bigg|_{#1}} + +%Vector representation \Vct{AB} : +\newcommand{\Vct}[1]{\overrightarrow{#1}} + +%################################### A-Kinematics : + +%Rotation vector definition \Rotation[R]{S} : +\newcommand{\Rotation}[2][R]{\Vct{\omega}_{#2/#1}} + +%Velocity vector definition \Vel[R]{A}{S} : +\newcommand{\Vel}[3][R]{\Vct{v}_{#2\in #3/#1}} + +%Transport formula for velocities \VARK[R]{A}{B}{S} : +\newcommand{\VARK}[4][R]{\Vel[#1]{#3}{#4}=\Vel[#1]{#2}{#4}+\Rotation[#1]{#4}\times\Vct{#2 #3}} + +%################################### B-Statics : + +%Force vector definition \Force[S]{Ext} : +\newcommand{\Force}[2][S]{\Vct{F}_{#2\rightarrow #1}} + +%Moment vector definition with force precision \Moment[S]{Ext}{A} : +\newcommand{\Moment}[3][S]{\Vct{M}_{#3}(\Vct{F}_{#2\rightarrow #1})} + +%Moment vector definition without force precision \Gmoment{Force}{A} : +\newcommand{\Gmoment}[2]{\Vct{M}_{#2}(#1)} + +%Transport formula for moments with force precision \VARS[S]{A}{B}{Ext} : +\newcommand{\VARS}[4][S]{\Moment[#1]{#4}{#3}=\Moment[#1]{#4}{#2}+\Force[#1]{#4}\times\Vct{#2 #3}} + +%Transport formula for moments without force precision \GVARS{Force}{A}{B} : +\newcommand{\GVARS}[3]{\Gmoment{#1}{#3}=\Gmoment{#1}{#2}+{#1}\times\Vct{#2 #3}} + +%Volumetric force resultant \Vnet[S]{f}{Ext} : +\newcommand{\Vnet}[3][S]{\iiint_{M \in #1}\Vct{#2}_{#3\rightarrow #1}(M)dm} + +%Volumetric force resultant with explicit volume \VVnet[S]{f}{Ext} : +\newcommand{\VVnet}[3][S]{\iiint_{M \in #1}\rho(M)\Vct{#2}_{#3\rightarrow #1}(M)dV} + +%Surface force resultant \Snet[S]{T}{Ext} : +\newcommand{\Snet}[3][S]{\iint_{M \in \partial #1}\Vct{#2}_{#3\rightarrow #1}(M)dS} + +%Surface force resultant with explicit normal \SSnet[S]{T}{Ext}{n} : +\newcommand{\SSnet}[4][S]{\iint_{M \in \partial #1}{#2}_{#3\rightarrow #1}(M)\Vct{#4}dS} + +%################################### C-Kinetics : + +%Momentum vector definition \Psr[R]{S} : +\newcommand{\Psr}[2][R]{\Vct{p}_{#2/#1}} + +%Momentum vector 2nd definition \Mv[R]{S} : +\newcommand{\Mv}[2][R]{m_{#2}\Vel[#1]{G}{#2}} + +%Angular momentum integral def \Lmi[R]{A}{S}: +\newcommand{\Lmi}[3][R]{\int_{M \in {#3}}\Vct{#2 M}\times \Vel[#1]{M}{#3} dm} + +%Angular momentum definition \Lm[R]{A}{S} : +\newcommand{\Lm}[3][R]{\Vct{L}_{#2, #3/#1}} + +%Transport formula for angular momenta \VARC[R]{A}{B}{S} : +\newcommand{\VARC}[4][R]{\Lm[#1]{#3}{#4}=\Lm[#1]{#2}{#4}+\Psr[#1]{#4}\times\Vct{#2 #3}} + +%Alternate transport formula for angular momenta \AVARC[R]{A}{B}{S} : +\newcommand{\AVARC}[4][R]{\Lm[#1]{#3}{#4}=\Lm[#1]{#2}{#4}+\Mv[#1]{#4}\times\Vct{#2 #3}} + +%Inertia tensor definition \Inertia[R]{A}{S} : +\newcommand{\Inertia}[3][R]{\overline{\overline{I}}_{#2}(#3/#1)} + +%Angular momentum general definition on arbitrary point \LA[R]{A}{S} : +\newcommand{\LA}[3][R]{m_{#3}\Vct{#2 G}\times \Vel[#1]{G}{#3}+\Inertia[#1]{#2}{#3} \cdot \Rotation[#1]{#3}} + +%Angular momentum general definition on fixed point and/or center of gravity \LF[R]{A}{S} : +\newcommand{\LF}[3][R]{\Inertia[#1]{#2}{#3} \cdot \Rotation[#1]{#3}} + +%Transport inertia tensor from G to A \Ip[S]{G}{A} : +\newcommand{\Ip}[3][S]{\overline{\overline{I}}_{\Vct{#3 #2}}(#1)} + +%Huygens formula \Huygens[R]{G}{A}{S} : +\newcommand{\Huygens}[4][R]{\Inertia[#1]{#3}{#4}=\Inertia[#1]{#2}{#4}+ \Ip[#4]{#2}{#3}} + +%Standard inertia tensor explicit expression \InertiaE[R]{A}{S} : +\newcommand{\InertiaE}[3][R]{\begin{Bmatrix} +A_{#3} & -D_{#3} & -E_{#3} \\ +-D_{#3} & B_{#3} & -F_{#3} \\ +-E_{#3} & -F_{#3} & C_{#3} +\end{Bmatrix}_{ (#3 / #1) }} + +%################################### C-Dynamics : + +%Acceleration vector definition \Acc[R]{A}{S} : +\newcommand{\Acc}[3][R]{\Vct{\Gamma}_{#2\in #3/#1}} + +%Acceleration vector differential definition \Accd[R]{A}{S} : +\newcommand{\Accd}[3][R]{\Dex[#1]{\Vel[#1]{#2}{#3}}} + +%Coriolis acceleration vector \Coriolis{R_0}{R_1}{A}{S} : +\newcommand{\Coriolis}[4]{2\Rotation[#1]{#2}\times\Vel[#2]{#3}{#4}} + +%Transport acceleration vector \Entr{R_0}{R_1}{O}{A} : +\newcommand{\Entr}[4]{\Acc[#1]{#3}{#2}+\Rotation[#1]{#2}\times(\Rotation[#1]{#2}\times \Vct{#3 #4})+\Dex[#1]{\Rotation[#1]{#2}}\times\Vct{#3 #4}} + +%Acceleration momentum vector definition \Am[R]{S} : +\newcommand{\Am}[2][R]{\Vct{d}_{#2/#1}} + +%Acceleration momentum vector 2nd definition \Amg[R]{S} : +\newcommand{\Amg}[2][R]{m_{#2}\Acc[#1]{G}{#2}} + +%Dynamic momentum integral def \IDelta[R]{A}{S}: +\newcommand{\IDelta}[3][R]{\int_{M \in {#3}}\Vct{#2 M}\times \Acc[#1]{M}{#3} dm} + +%Dynamic momentum definition \ADelta[R]{A}{S} : +\newcommand{\ADelta}[3][R]{\Vct{\delta}_{#2, #3/#1}} + +%Transport formula for dynamic momenta \VARD[R]{A}{B}{S} : +\newcommand{\VARD}[4][R]{\ADelta[#1]{#3}{#4}=\ADelta[#1]{#2}{#4}+\Am[#1]{#4}\times\Vct{#2 #3}} + +%Alternate transport formula for dynamic momenta \AARD[R]{A}{B}{S} : +\newcommand{\AVARD}[4][R]{\ADelta[#1]{#3}{#4}=\ADelta[#1]{#2}{#4}+\Amg[#1]{#4}\times\Vct{#2 #3}} + +%Dynamic momentum general expression \EDelta[R]{A}{S} : +\newcommand{\EDelta}[3][R]{\Dex[#1]{\Lm[#1]{#2}{#3}}+m_{#3}\Vct{v}_{#2/#1}\times\Vct{v}_{G/#1}} + +%Dynamic momentum general expression for fixed point or center of gravity \FDelta[R]{G}{S} : +\newcommand{\FDelta}[3][R]{\Dex[#1]{\Lm[#1]{#2}{#3}}} + +%################################### D-Screw field representation : + +%Kinematic screw field on a point \Ktor[R]{A}{S}: +\newcommand{\Ktor}[3][R]{\begin{Bmatrix} +\mathscr{V}_{({#3}/{#1})} +\end{Bmatrix}= +\begin{Bmatrix} +\Rotation[#3]{#1} \\ +\Vel[#1]{#2}{#3} +\end{Bmatrix}_{#2}} + +%Explicit kinematic screw field for a support \EKtor[R]{A}{S} : +\newcommand{\EKtor}[3][R]{\begin{Bmatrix} +\mathscr{V}_{({#3}/{#1})} +\end{Bmatrix}= +\begin{Bmatrix} +\omega_{x,({#3}/{#1})} & v_{x,(#2\in #3/#1)} \\ +\omega_{y,({#3}/{#1})} & v_{y,(#2\in #3/#1)} \\ +\omega_{z,({#3}/{#1})} & v_{z,(#2\in #3/#1)} +\end{Bmatrix}_{#2}} + +%Static screw field on a point \Stor[S]{Ext}{A}: +\newcommand{\Stor}[3][S]{\begin{Bmatrix} +\mathscr{T}_{({#2}\rightarrow{#1})} +\end{Bmatrix}= +\begin{Bmatrix} +\Force[#1]{#2} \\ +\Moment[#1]{#2}{#3} +\end{Bmatrix}_{#3}} + +%Kinetic screw field on a point \Ctor[R]{A}{S}: +\newcommand{\Ctor}[3][R]{\begin{Bmatrix} +\mathscr{C}_{({#3}/{#1})} +\end{Bmatrix}= +\begin{Bmatrix} +\Psr[#3]{#1} \\ +\Lm[#1]{#2}{#3} +\end{Bmatrix}_{#2}} + +%Dynamic screw field on a point \Dtor[R]{A}{S}: +\newcommand{\Dtor}[3][R]{\begin{Bmatrix} +\mathscr{D}_{({#3}/{#1})} +\end{Bmatrix}= +\begin{Bmatrix} +\Am[#3]{#1} \\ +\ADelta[#1]{#2}{#3} +\end{Bmatrix}_{#2}} + +%Explicit static screw field for a support \Ltor{S_1}{S_2}{A} : +\newcommand{\Ltor}[3]{\begin{Bmatrix} +\mathscr{L}_{({#1}\rightarrow{#2})} +\end{Bmatrix}= +\begin{Bmatrix} +X_{({#1}\rightarrow{#2})} & L_{({#1}\rightarrow{#2})} \\ +Y_{({#1}\rightarrow{#2})} & M_{({#1}\rightarrow{#2})} \\ +Z_{({#1}\rightarrow{#2})} & N_{({#1}\rightarrow{#2})} +\end{Bmatrix}_{#3}} + +%Explicit static screw field for a planar support \Lptor{S_1}{S_2}{A} : +\newcommand{\Lptor}[3]{\begin{Bmatrix} +\mathscr{L}_{({#1}\rightarrow{#2})} +\end{Bmatrix}= +\begin{Bmatrix} +X_{({#1}\rightarrow{#2})} & 0 \\ +Y_{({#1}\rightarrow{#2})} & 0 \\ +0 & M_{({#1}\rightarrow{#2})} +\end{Bmatrix}_{#3}} + +%Empty screw field template on a point \Ftor[S/R]{W}{A}{B}{O}: +\newcommand{\Ftor}[5][Ref]{\begin{Bmatrix} +\mathscr{#2}_{#1} +\end{Bmatrix}= +\begin{Bmatrix} +{#3} \\ +{#4} +\end{Bmatrix}_{#5}} + +%Empty explicit screw field template on a point \LFtor[S/R]{W}{X}{Y}{Z}{X}{Y}{Z}{0}: +\newcommand{\LFtor}[9][Ref]{\begin{Bmatrix} +\mathscr{#2}_{#1} +\end{Bmatrix}= +\begin{Bmatrix} +{#3} & {#6} \\ +{#4} & {#7} \\ +{#5} & {#8} +\end{Bmatrix}_{#9}} + +%################################### E-Energy and power : + +%Power delivered from ext to S \Pow[R]{S}{Ext} : +\newcommand{\Pow}[3][R]{P_{(#3 \rightarrow #2/#1)}} + +%Power delivered from ext to S, screw expression \Ptor[R]{S}{Ext} : +\newcommand{\Ptor}[3][R]{\begin{Bmatrix} +\mathscr{T}_{({#3}\rightarrow{#2})} +\end{Bmatrix} \otimes \begin{Bmatrix} +\mathscr{V}_{({#2}/{#1})} +\end{Bmatrix}} + +%Power delivered from ext to S, explicit expression \Power[R]{A}{S}{Ext} : +\newcommand{\Power}[4][R]{\Force[#3]{#4}\cdot\Vel[#1]{#2}{#3} + \Gmoment{\Force[#3]{#4}}{#2}\cdot \Rotation[#1]{#3}} + +%Power delivered from ext to S, integral expression \IPow[R]{S}{f} : +\newcommand{\IPow}[3][R]{\int_{M \in #2} \Vct{#3}(M)\cdot \Vel[#1]{M}{#2} dm} + +%Internal support power \LPow{S_1}{S_2} : +\newcommand{\LPow}[2]{P_{(#1 \leftrightarrow #2)}} + +%Internal support power, screw definition \PLtor{S_1}{S_2} : +\newcommand{\PLtor}[2]{\begin{Bmatrix} +\mathscr{T}_{({#1}\rightarrow{#2})} +\end{Bmatrix} \otimes \begin{Bmatrix} +\mathscr{V}_{({#2}/{#1})} +\end{Bmatrix}} + +%Kinetic energy, integral expression \KE[R]{S}: +\newcommand{\KE}[2][R]{ \frac{1}{2}\int_{M \in #2} \Vel[#1]{M}{#2}^{2}dm } + +%Kinetic energy, screw expression \KEtor[R]{S}: +\newcommand{\KEtor}[2][R]{\frac{1}{2} \begin{Bmatrix} +\mathscr{C}_{(#2 / #1)} +\end{Bmatrix} \otimes \begin{Bmatrix} +\mathscr{V}_{(#2 / #1)} +\end{Bmatrix}} + +%Kinetic energy, translation only \KineticT[R]{A}{S}: +\newcommand{\KineticT}[3][R]{\frac{1}{2}m_{#3}\Vel[#1]{#2}{#3}^{2}} + +%Kinetic energy, rotation about center only \KineticR[R]{C}{S}: +\newcommand{\KineticR}[3][R]{\frac{1}{2}\Rotation[#1]{#3} \cdot (\Inertia[#1]{#2}{#3} \cdot \Rotation[#1]{#3})} + +%Kinetic energy, general expression \Kinetic[R]{A}{S}: +\newcommand{\Kinetic}[3][R]{\KineticT[#1]{#2}{#3} + \KineticR[#1]{#2}{#3} + m_{#3} \Rotation[#1]{#3} \cdot( \Vct{#2 G} \times \Vel[#1]{#2}{#3}) } + +%Kinetic energy written in G \KineticG[R]{S}: +\newcommand{\KineticG}[2][R]{\KineticT[#1]{G}{#2} + \KineticR[#1]{G}{#2}} + +\endinput
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