Analysis of non-linearly constrained non-holonomic multibody systems

Abstract

This paper presents a method for studying multibody systems subjected to non-linear non-holonomic constraints. The method employs a modified form of Kane's equations and a differentiated form of the constraint equations. Kane's equations are modified by the inclusion of generalized constraint forces, and the differentiated constraint equations become linear in higher derivatives of the generalized coordinates. It is observed that the generalized constraint force array is proportional to the transpose of the matrix of coefficients of the constraint equations. Using this relationship the governing equations are reduced to a consistent set of differential equations through a multiplication with an orthogonal complement of the constraint equation matrix. The method is illustrated with the classical Appell-Hamel problem. © 1990.