New hamiltonian formulation of rheonomous affine constraints based on the rheonomous bracket

This paper presents a Hamiltonian formulation technique for rheonomous affine constraints. We first explain some concepts on rheonomous affine constraints and introduce the rheonomous bracket. Next, a complete nonholonomicity condition for the rheonomous affine constraints is shown. Then, we derive the nonholonomic Hamiltonian system with rheonomous affine constraints (NHSRAC) via a transformation and model reduction for the expanded Hamiltonian system defined on the expanded phase space. After that, a passivity condition for the NHSRAC with the control input term and the output equation is investigated. Finally, we show a physical example in order to verify our new results.