Canonical Approach to Multibody Systems Using Redundant Coordinates

Summary

The utility of the methods of classical dynamics as tools for formulating equations of motion is investigated. A new projection method, euitable for a general class of multibody systems, is also presented. In applying this alternative method, every body of the system is first described by its own arbitrarily chosen position and velocity variables, after which the constraints governing the system are introduced. These constraint relations are linear functions of the velocity variables. They are used to construct projection operators describing the relationship between the unconstrained and constrained system. The method allows the equations of motion to be split into two sets: one describing the motion of the constrained system, the other yielding the reactive forces. The inverse mass matrix of the constrained system is expressed in terms of an inverse matrix of lower order, and in some systems a set of explicit differential equations can be obtained. An important feature of this method is that geometric singularities are easily avoided.