2012 年 78 巻 789 号 p. 1428-1439
This paper describes the application of the canonical theory to a constrained multibody system in the absolute nodal coordinate formulation. In the canonical theory, the constraints make it difficult to formulate the equations of motion because of the primary constraints of the Hamiltonian system. In order to solve this problem, the Dirac's approach with Poisson's bracket is used to derive the canonical equations. The governing equation of multibody systems with constraints is usually expressed as the differential-algebraic equations. In contrast, the canonical theory for the constrained system proposed by Dirac leads to the ordinary differential equations without constraints. In this study, it is demonstrated that the linear and the nonlinear canonical equations which the elastic force is formulated in the element coordinate system. The natural frequency and the eigenmode of the beam are obtained by the linearized canonical equations. These results show that the natural frequency and the eigenmode satisfy the boundary conditions introduced by the constraints. Moreover, the numerical examples of the nonlinear problems with the canonical equation and the differential-algebraic equation are presented in order to verify the proposed formulation.