On the Geometry of Nonholonomic Dynamics

Abstract

The formulation and derivation of equations of motion for finite degree-of-freedom nonholonomic systems, is discussed. The starting point is Newton’s equation of motion in the 3K-dimensional unconstrained configuration space of K particles. Constraints represent knowledge that motion is only possible along some directions in the local tangent spaces. Only projections of the 3K-dimensional vector equation onto these allowed directions are of interest. The formalism is essentially that of Kane-Appell cast into an abstract form. It is shown to give the same equations as Hamel’s generalization of Lagrange’s method. The algorithmic advantage of the Kane-Appell projection approach is stressed.