Dynamics Notes

This will be the localized place for all future dynamics notes, however, much of my dynamics notes are currently located on the notes page for my analytical dynamics class.

Table of Contents

Equations of Motion

Cannonical Form Given in Featherstone's Book

Unlabeled Form in Kanes Book

Forms Labeled in Robinovitch's Slides

Forward Dynamics

  • \ddot{\phi} = M(\phi)^{-1}T^{mus} + M(\phi)^{-1}V(\phi, \dot{\phi}) +  M(\phi)^{-1}G(\phi)

Inverse Dynamics

  • T^{mus} = M(\phi)\ddot{\phi} + V(\phi, \dot{\phi}) + G(\phi)

Mass Matrix

The formal definition for a mass matrix M is

T = \frac{1}{2} \dot{q}^{T} M \dot{q}

where

Nonholonomic system

A nonholonomic system is a system whose state depends on the path taken in order to achieve it. (Path dependent system)

A constraint which does not reduce the degrees of freedom (Knowing one generalized coordinate and the constraint allows solving for the other coordinate is a holonomic system, ie two points connected by a massless rod)


Sources