Lagrangian reduction of generalized nonholonomic systems

Abstract

In this paper we study the Lagrangian reduction of generalized nonholonomic systems (GNHS) with symmetry. We restrict ourselves to those GNHS, defined on a configuration space Q, with kinematic constraints given by a general submanifold CK ⊂ T Q, and variational constraints given by a distribution CV on Q. We develop a reduction procedure that is similar to that for nonholonomic systems satisfying d'Alembert's principle, i.e. with CK a distribution and CV = CK. Special care is taken in identifying the geometrical structures and mappings involved. We illustrate the general theory with an example.