Derivation and analysis of nonholonomic Hamiltonian systems with affine constraints

In this paper, we introduce and analyze Hamiltonian systems subject to nonholonomic affine constraints. In our previous work, we researched nonholonomic dynamic systems with affine constraints (NDSAC) from the Lagrangian perspective, and derived some interesting properties on the NDSAC. However, Hamiltonian approach is also important in terms of dissipativity, passivity and so on. We first explain Hamiltonian systems on both the phase space and the expanded phase space. Then, we derive nonholonomic Hamiltonian systems with affine constraints (NHSAC) and investigate passivity of the NHSAC. Finally, a physical example is illustrated to confirm the results.