[AMR] Fix typos, improve space usage some more

This commit is contained in:
2026-08-01 11:31:44 +02:00
parent 55030a0d0a
commit c80452f383
8 changed files with 15 additions and 14 deletions
@@ -1,6 +1,6 @@
\subsection{Rigid Body Dynamics}
\label{sec:rigid-body-dynamics}
\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:
\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), in body frame:
\begin{align*}
{_B}\vec{F} & = \sum {_B}\vec{F}_i = m({_B} \vec{\dot{v}}_{CoM}) + m_B \vec{\omega} \times {_B}\vec{v}_{CoM} \\
{_B}\vec{T} & = \sum {_B}\vec{T}_i = \mat{I}({_B} \vec{\dot{\omega}}) + {_B} \vec{\omega} \times \mat{I}_B\vec{\omega}
@@ -6,10 +6,12 @@
\bi{Wheel constraints} $v_i = \omega_i r_i$ ($r_i$ constraints)
\begin{itemize}
\item \textit{Driving straight} all $\vec{v}$ equal
\item \textit{Driving straight} all $\vec{v}$ equal (ICR: R.Cent.)
\item \textit{Turning} Wheel axis must intersect the \bi{Instant Centre of Rotation} (ICR) of vehicle,
speeds: $v_i \div R_i = \Omega$ ($R_i$ = dist. wheel-ICR; $\Omega$: vehicle rotation rate (around ICR))
\end{itemize}
To compute ICR, use $v_i \div R_i = \Omega$ and similarity.
Below: $\alpha$, $l$ pos in frame, $\beta$ rot at that pos ($z$-ax).
To compute $\vec{c}$ in $\vec{c} \cdot {_B}\vec{v}_{WB} = \omega$
(For multiple wheels, construct mat. from this)