Model reduction method for nonholonomic mechanical systems with semidirect product symmetry

In this paper, a method of deriving reduced dynamic models for a class of nonholonomically constrained systems that are described on semidirect products is developed. The theory is built upon the Lagrangian reduction method for unconstrained systems on semidirect products and the Lagrangian reduction theory for nonholonomic systems defined on symmetry groups. The reduction is achieved by first applying Hamilton's variational principle and then imposing the nonholonomic constraints. The theory is then applied to Chaplygin's gyro type of spherical robots.