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Birkhoffian symplectic algorithms derived from Hamiltonian symplectic algorithms |
| Xin-Lei Kong(孔新雷)1, Hui-Bin Wu(吴惠彬)2, Feng-Xiang Mei(梅凤翔)3 |
1. College of Science, North China University of Technology, Beijing 100144, China;
2. School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China;
3. School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China |
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Abstract In this paper, we focus on the construction of structure preserving algorithms for Birkhoffian systems, based on existing symplectic schemes for the Hamiltonian equations. The key of the method is to seek an invertible transformation which drives the Birkhoffian equations reduce to the Hamiltonian equations. When there exists such a transformation, applying the corresponding inverse map to symplectic discretization of the Hamiltonian equations, then resulting difference schemes are verified to be Birkhoffian symplectic for the original Birkhoffian equations. To illustrate the operation process of the method, we construct several desirable algorithms for the linear damped oscillator and the single pendulum with linear dissipation respectively. All of them exhibit excellent numerical behavior, especially in preserving conserved quantities.
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Received: 26 July 2015
Revised: 31 August 2015
Accepted manuscript online:
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PACS:
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02.40.Yy
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(Geometric mechanics)
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02.60.Cb
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(Numerical simulation; solution of equations)
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45.20.Jj
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(Lagrangian and Hamiltonian mechanics)
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| Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11272050), the Excellent Young Teachers Program of North China University of Technology (Grant No. XN132), and the Construction Plan for Innovative Research Team of North China University of Technology (Grant No. XN129). |
Corresponding Authors:
Xin-Lei Kong
E-mail: kongxinlei@ncut.edu.cn
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Cite this article:
Xin-Lei Kong(孔新雷), Hui-Bin Wu(吴惠彬), Feng-Xiang Mei(梅凤翔) Birkhoffian symplectic algorithms derived from Hamiltonian symplectic algorithms 2016 Chin. Phys. B 25 010203
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