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Article

A Symplectic Algorithm for Constrained Hamiltonian Systems

by
Jingli Fu
1,
Lijun Zhang
2,3,*,
Shan Cao
4,
Chun Xiang
5 and
Weijia Zao
6
1
College of Information and Control Engineering, Shandong Vocational University of Foreign Affairs, Weihai 264504, China
2
Department of Mathematics, Shandong University of Science and Technology, Qingdao 266590, China
3
International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Mmabatho X2046, South Africa
4
Institute of Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China
5
College of Mechanical and Automotive Engineering, Zhejiang University of Water Resources and Electric Power, Hangzhou 310018, China
6
Department of Mathematics, Qingdao University, Qingdao 266071, China
*
Author to whom correspondence should be addressed.
Axioms 2022, 11(5), 217; https://doi.org/10.3390/axioms11050217
Submission received: 18 April 2022 / Revised: 26 April 2022 / Accepted: 30 April 2022 / Published: 7 May 2022
(This article belongs to the Special Issue 10th Anniversary of Axioms: Mathematical Physics)
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Abstract

In this paper, a symplectic algorithm is utilized to investigate constrained Hamiltonian systems. However, the symplectic method cannot be applied directly to the constrained Hamiltonian equations due to the non-canonicity. We firstly discuss the canonicalization method of the constrained Hamiltonian systems. The symplectic method is used to constrain Hamiltonian systems on the basis of the canonicalization, and then the numerical simulation of the system is carried out. An example is presented to illustrate the application of the results. By using the symplectic method of constrained Hamiltonian systems, one can solve the singular dynamic problems of nonconservative constrained mechanical systems, nonholonomic constrained mechanical systems as well as physical problems in quantum dynamics, and also available in many electromechanical coupled systems.
Keywords: constrained Hamiltonian system; canonicalization; symplectic method; numerical simulation constrained Hamiltonian system; canonicalization; symplectic method; numerical simulation

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MDPI and ACS Style

Fu, J.; Zhang, L.; Cao, S.; Xiang, C.; Zao, W. A Symplectic Algorithm for Constrained Hamiltonian Systems. Axioms 2022, 11, 217. https://doi.org/10.3390/axioms11050217

AMA Style

Fu J, Zhang L, Cao S, Xiang C, Zao W. A Symplectic Algorithm for Constrained Hamiltonian Systems. Axioms. 2022; 11(5):217. https://doi.org/10.3390/axioms11050217

Chicago/Turabian Style

Fu, Jingli, Lijun Zhang, Shan Cao, Chun Xiang, and Weijia Zao. 2022. "A Symplectic Algorithm for Constrained Hamiltonian Systems" Axioms 11, no. 5: 217. https://doi.org/10.3390/axioms11050217

APA Style

Fu, J., Zhang, L., Cao, S., Xiang, C., & Zao, W. (2022). A Symplectic Algorithm for Constrained Hamiltonian Systems. Axioms, 11(5), 217. https://doi.org/10.3390/axioms11050217

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