Takehiko Kawase

Bond graph modelling of multibody dynamics and its symbolic scheme

Abstract A bond graph method of modelling multibody dynamics is demonstrated. Specifically, a symbolic generation scheme which fully utilizes the bond graph information is presented. It is also demonstrated that structural understanding and representation in bond graph theory is quite powerful for the modelling of such large scale systems, and that the non-energic multiport of junction structure, which is a multiport expression of the system structure, plays an important role, as first suggested by Paynter. The principal part of the proposed symbolic scheme, that is, the elimination of excess variables, is done through tearing and interconnection in the sense of Kron using newly defined causal and causal coefficient arrays.

A Duality Principle in Nonholonomic Mechanical Systems

The paper presents a duality principle in nonholonomic mechanical systems extensively utilizing Birkhoff’s idea of nonenergicness. It is shown that the nonenergic condition provides a structure of constrained mechanical systems specifically focusing on the nonholonomic systems, and that a duality principle is employed by analogy with Planck-Okada-Arsove’s theorem in network theory. Introducing connection matrices, a dual pair of constraints for velocities and forces is developed in a causal form to formulate required kinematical and dynamical relations associated with ideal constraints, and geometric properties of configuration subspaces are also investigated. It is finally demonstrated how reduced dynamical equations of the nonholonomic systems are derived with adjoint kinematical equations by exploiting the duality principle together with an illustrative example.