アファイン拘束を受ける非ホロノミックハミルトニアンシステムのモデリングと受動性解析

Abstract

In this paper, we introduce and analyze Hamiltonian systems subject to nonholonomic affine constraints. We first sum up some concepts of Hamiltonian systems defined on both the phase space and the expanded phase space. Next, we derive nonholonomic Hamiltonian systems with affine constraints (NHSAC) by using a transformation and reduction on the expanded phase space. Then, passivity of the NHSAC with the control input term and the output equation is investigated. Finally, a coin on a rotating table is illustrated to confirm the results as a physical example.