Unified approach to non-holonomic dynamics

Abstract

Dynamical problems subject to non-linear non-holonomic constraints are analyzed using the differential variational principles of Jourdain (JVP) and Gauss (GVP). In contrast with linear non-holonomic constraints which arise from passive contact or rolling constraints, non-linear non-holonomic constraints (NNHC) arise in problems where the constraints are actively imposed, such as control or servo-constraints, consideration of some first integrals as kinetic side conditions, or mathematical constraints without regard to their physical realizability. To date, such problems have been treated by various ad hoc and unrelated methods in a fragmented manner, without a unifying idea running through the various methods of approach. In the present paper, it is shown that by applying the JVP to velocity constraints, and the GVP to acceleration constraints, dynamical problems subject to NNHC can be handled in a uniform way. Both the method of constraint embedding (elimination of variations) and constraint adjoining (use of Lagrange multipliers) are used in analyzing the behavior of the dynamical system subject to NNHC.