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[AMR] Kinematics defs, better linking
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@@ -8,5 +8,8 @@ $ \begin{bmatrix}
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L_1 \sin(\theta_1) + L_2 \sin(\theta_1 + \theta_2)
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\end{bmatrix}$\\
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}
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With workspace (pos) $W$ for $\theta_1, \theta_2 \in [-\pi, \pi]$
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% TODO: Example? (w02s42 possibly)
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Similar for $n$R sys (more angles). Wspc $W$ $\theta_1, \theta_2 \in [-\pi, \pi]$.
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Last dim may be sum of angles. Jacobian: see \ref{sec:ms-lin}
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\shortdefinition[Singularity] Loss of deg of Freed. $\det(\mat{J}(\vec{\theta})) = 0$
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% TODO: Determinant computation
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@@ -1,4 +1,5 @@
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\subsection{Linearization}
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\label{sec:ms-lin}
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$\vec{f}(\vec{x}) \approx \vec{f}(\vec{\overline{x}}) + \mat{J}_{\vec{f}} \big|_{x = \overline{x}}(\vec{x} - \vec{\overline{x}})$, $f'$, no vec in 1D; $\vec{\overline{x}}$ lin. p.
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\shortdefinition[Jac.] $\mat{J}_{\vec{f}}$ rows for eq of $\vec{f}$ cols for vars of each eq.
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