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| The symplectic algorithms for Hamiltonian dynamic systems based on a new variational principle part I：the variational principle and the algorithms |
| Received:February 10, 2012 Revised:July 15, 2012 |
| View Full Text View/Add Comment Download reader |
| DOI：10.7511/jslx201304001 |
| KeyWord:symplectic Hamiltonian system variational principle action |
| Author | Institution |
| 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 |
| 彭海军 |
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 |
| 张洪武 |
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: |
| In this paper,a new variational principle is proposed for the finite dimensional autonomous Hamiltonian systems and four types of symplecitc numerical algorithms are constructed.A modified action is defined by using the new variational principle.Then,the approximated action is obtained by approximating the generalized coordinates and momenta by Lagrange polynomials within a time step,and approximating the time integrals by means of Gaussian quadrature.Based on the approximated action and by taking generalized coordinates or momenta as independent variables at each end of the time step,four types of symplecitc numerical algorithms are constructed.In this paper,the detailed procedure for the construction of the algorithms is given and the proof of symplectic property and the numerical performance of the algorithms will present in other papers. |
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