A comparison of vakonomic and nonholonomic dynamics for systems on Lie groups∗

We study relations between vakonomically and nonholonomically constrained dynamics for the same set of linear constraints for a Lagrangian system on a Lie group. We obtain necessary and sucient conditions under which a nonholomic trajectory is also a vakonomic one. Concrete example of a two-wheeled carriage with a shifted center of mass is discussed.