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| Symplectic algorithm for holonomic constrained systems based on the dual variable variational principle |
| Received:November 19, 2019 Revised:January 10, 2020 |
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| DOI：10.7511/jslx20191119001 |
| KeyWord:symplectic holonomic constraints Hamiltonian system dual variable |
| Author | Institution |
| 满淑敏 |
大连理工大学 工业装备结构分析国家重点实验室, 工程力学系, 大连 |
| 高强 |
大连理工大学 工业装备结构分析国家重点实验室, 工程力学系, 大连 |
| 钟万勰 |
大连理工大学 工业装备结构分析国家重点实验室, 工程力学系, 大连 |
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| Abstract: |
| Based on the dual-variable variational principle,symplectic algorithms for Hamiltonian systems with holonomic constraints are derived by taking the displacements at two ends of time intervals as the independent variables.The approximation of the action integral is obtained by approximating the displacements,momentums and Lagrange multipliers by Lagrange polynomial,by implementing Gauss quadrature rule on the integral corresponding to the Hamiltonian and by implementing Lobatto quadrature rule on the integral corresponding to constraints.Based on this approximation and using the dual-variable variational principle,the problem of solving holonomic constrained Hamiltonian systems is transformed into solving a set of nonlinear equations.The resulting algorithm is symplectic,has high convergence order and can satisfy the holonomic constraints with high-precision at interpolation points of the approximate displacements.The convergence order and numerical properties of the symplectic algorithms are shown by numerical examples. |
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