On the geometry of nonholomonic dynamics.

Authors: Essén, H.
Document Type: Article
Pubstate: Published
Journal: Journal of applied mechanics
Volume: 61   689-694
Year: 1994


This article discusses the formulation and derivation of equations of motion for finite degree of freedom mechanical systems with non-holonomic constraints. The vectorial Newtonian equations of motion are taken as starting point. For $K$ particles this gives a $3K$-dimensional configuration space. Constraints may then be seen as representing knowledge that motion is only possible along some of the directions in the local tangent space at each point of this space. Only the projections of the $3K$-dimensional vector equation onto these allowed directions will then be of interest. There is no need for any further principles or postulates. The formalism, which essentially is that of Kane cast into a more abstract form, is shown to give the same equations of motion as the traditional Lagrangian method when it is generalized to quasi-coordinates. The computational advantage of the Kane-type direct projection approach is stressed and exemplified.