Modeling and passivity analysis of nonholonomic Hamiltonian systems with rheonomous affine constraints

This paper is devoted to modeling and theoretical analysis of Hamiltonian systems subject to nonholonomic rheonomous affine constraints. We first define rheonomous affine constraints and explain geometric representation of them. Next, a complete nonholonomicity condition for the rheonomous affine constraints is developed in terms of the rheonomous bracket. Then, the nonholonomic Hamiltonian system with rheonomous affine constraints (NHSRAC) is derived via a transformation and model reduction for the expanded Hamiltonian system defined on the expanded phase space. After that, we investigate passivity of the NHSRAC with the control input term and the output equation. Finally, in order to confirm the application potentiality of our new results, we show an example, a radius-variable ball on rotating table with a time-varying angular velocity.

► A complete nonholonomicity condition for the rheonomous affine constraints is derived in terms of the rheonomous bracket.
► We introduce the nonholonomic Hamiltonian system with rheonomous affine constraints (NHSRAC).
► A passivity condition for the NHSRAC with the control input term and the output equation is shown.
► We apply our new results on the NHSRAC to a physical example.