327 正準理論に基づいたマルチボディシステムの定式化

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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. In general, the governing equation of multibody systems with constraints is 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. 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 time histories of the beam subjected to the periodic excitation in vertical direction is calculated by the nonlinear analysis with the canonical equation. The result of nonlinear analysis shows the characteristic dynamic behavior in the large deformation problem.
2011-09-05