This paper presents a geometric description of Lagrangian and Hamiltonian systems on Lie affgebroids subject to affine nonholonomic constraints. We define the notion of nonholonomically constrained system, and characterize regularity conditions that guarantee that the dynamics of the system can be obtained as a suitable projection of the unconstrained dynamics. It is shown that one can define a...

Control systems with nonholonomic motion constraints have been extensively studied in the recent years, particularly in the context of robotics. Robotic manipulators, especially mobile ones, are described by complicated models about which there is likely to be significant uncertainty [4]. This is just one source of motivation for studying the challenging problem of controlling nonholonomic mech...

This paper applies the recently developed theory of discrete nonholonomic mechanics to the study of discrete nonholonomic left-invariant dynamics on Lie groups. The theory is illustrated with the discrete versions of two classical nonholonomic systems, the Suslov top and the Chaplygin sleigh. The preservation of the reduced energy by the discrete flow is observed and the discrete momentum conse...

We discuss an extension of the Hamilton–Jacobi theory to nonholonomic mechanics with a particular interest in its application to exactly integrating the equations of motion. We give an intrinsic proof of a nonholonomic analogue of the Hamilton–Jacobi theorem. Our intrinsic proof clarifies the difference from the conventional Hamilton–Jacobi theory for unconstrained systems. The proof also helps...

In the first part of the paper we present a new point of view on the geometry of nonholonomic mechanical systems with linear and affine constraints. The main geometric object of the paper is the nonholonomic connection on the distribution of constraints. By using this connection we obtain the Newton forms of Lagrange–d’Alembert equations for nonholonomic mechanical systems with linear and affin...