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10 lines
597 B
TeX
10 lines
597 B
TeX
\subsection{Rigid Body Dynamics}
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\label{sec:rigid-body-dynamics}
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\shortdefinition[Newton II] For fin. body w/ mass $m$ and inertia mat. $I$, with force $\vec{F}$ and torque $\vec{T}$ on \bi{Centre of Mass} (CoM), expressed in body frame:
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\begin{align*}
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{_B}\vec{F} &= \sum {_B}\vec{F}_i = m({_B} \vec{\dot{v}}_{CoM}) + m_B \vec{\omega} \times {_B}\vec{v}_{CoM} \\
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{_B}\vec{T} &= \sum {_B}\vec{T}_i = \mat{I}({_B} \vec{\dot{\omega}}) + {_B} \vec{\omega} \times \mat{I}_B\vec{\omega}
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\end{align*}
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${_B} \vec{v}_{CoM}$ vel. of CoM, ${_B}\omega$ rot. speed; both w.r.t. world frame
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