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z8qfHejY%l$_4F36Jxtm`ItmBi80>|EFbE?s1QW0m#-Jbe!2leBQ7-Bin1o@*VGil< zJ4zCfv+vular6f|^*b~!a{M=c%G-2DNSsgi!*1wXB-1%KmGs6XXb;d@iQQ0)c2 zZskTO%b;wDvOdZkQkF~EI`xmwPAbc)Y_YQ5%HAt`uk5|D?aH<*JFe`wvf0XJEB9Vm zYGtXFRaRD6{XVnB$`)%$qR$5WxD670dC}7fiLRgav{Irw4?HzWJnv&qt0Zo};%T+S zV;4L%NqqbZPk+r4fBlZ9H4?wv>#0SO@@Jk}CF$w$)F#QuFP_#)a{9KXc1b?H>uH@N z=Z8IYNSYQst(SCg`aL#C`qjUlIwgH|&eKN8I!c~4Np|g(r_GW#PoH#)WN%_> Y3UhQ}a+gg`2nh->HZTe$B}Gq03iJAV=Kufz diff --git a/electives/others/amr/parts/01_kinematics/00_intro.tex b/electives/others/amr/parts/01_kinematics/00_intro.tex index df988ac..63d1bb9 100644 --- a/electives/others/amr/parts/01_kinematics/00_intro.tex +++ b/electives/others/amr/parts/01_kinematics/00_intro.tex @@ -6,21 +6,21 @@ $_{\color{blue}\fbox{W}}\,\vec{t}\,_{\color{red}\fbox{B}} = \, _{\color{blue}\fb \shortdefinition[State vector] $x_R$: $x$, $v$ of rob in $W$, pos of sensors -\shortdefinition[Rot. Mat.] $\mat{R}_{z} = \begin{bmatrix} +\shortdefinition[Rot. Mat.] $\mat{R}_{z}(\psi) = \begin{bmatrix} c(\psi) & -s(\psi) & 0 \\ s(\psi) & c(\psi) & 0 \\ 0 & 0 & 1 \end{bmatrix}$\\ $\mat{R}_y(\theta) = \begin{bmatrix} - c(\psi) & 0 & s(\psi) \\ + c(\theta) & 0 & s(\theta) \\ 0 & 1 & 0 \\ - -s(\psi) & 0 & c(\psi) \\ - \end{bmatrix} + -s(\theta) & 0 & c(\theta) \\ + \end{bmatrix}; \mat{R}_x(\varphi) \begin{bmatrix} 1 & 0 & 0 \\ - 0 & c(\psi) & -s(\psi) \\ - 0 & s(\psi) & c(\psi) + 0 & c(\varphi) & -s(\varphi) \\ + 0 & s(\varphi) & c(\varphi) \end{bmatrix}$ \shortremark Application: ${_W} \vec{a} = \mat{R}_{WB} {_B} \vec{a}$