Poisson theory and integration method for a dynamical system of relative motion

doi:10.1088/1674-1056/20/2/024501

中国物理B ›› 2011, Vol. 20 ›› Issue (2): 24501-024501.doi: 10.1088/1674-1056/20/2/024501

• CLASSICAL AREAS OF PHENOMENOLOGY • 上一篇下一篇

Poisson theory and integration method for a dynamical system of relative motion

张毅¹, 尚玫²

(1)College of Civil Engineering, Suzhou University of Science and Technology, Suzhou 215011, China; (2)School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China

收稿日期:2010-07-30 修回日期:2010-08-21 出版日期:2011-02-15 发布日期:2011-02-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 10972151).

Poisson theory and integration method for a dynamical system of relative motion

Zhang Yi(张毅)^a)^† and Shang Mei(尚玫)^b)

^a College of Civil Engineering, Suzhou University of Science and Technology, Suzhou 215011, China; ^b School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China

Received:2010-07-30 Revised:2010-08-21 Online:2011-02-15 Published:2011-02-15
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 10972151).

摘要/Abstract

摘要： This paper focuses on studying the Poisson theory and the integration method of dynamics of relative motion. Equations of a dynamical system of relative motion in phase space are given. Poisson theory of the system is established. The Jacobi last multiplier of the system is defined, and the relation between the Jacobi last multiplier and the first integrals of the system is studied. Our research shows that for a dynamical system of relative motion, whose configuration is determined by n generalized coordinates, the solution of the system can be found by using the Jacobi last multiplier if (2n-1) first integrals of the system are known. At the end of the paper, an example is given to illustrate the application of the results.

Abstract: This paper focuses on studying the Poisson theory and the integration method of dynamics of relative motion. Equations of a dynamical system of relative motion in phase space are given. Poisson theory of the system is established. The Jacobi last multiplier of the system is defined, and the relation between the Jacobi last multiplier and the first integrals of the system is studied. Our research shows that for a dynamical system of relative motion, whose configuration is determined by n generalized coordinates, the solution of the system can be found by using the Jacobi last multiplier if (2n-1) first integrals of the system are known. At the end of the paper, an example is given to illustrate the application of the results.

Key words: dynamics of relative motion, Poisson theory, method of integration, Jacobi last multiplier

中图分类号: (Lagrangian and Hamiltonian mechanics)

45.20.Jj

02.30.Hq (Ordinary differential equations) 02.30.Jr (Partial differential equations)

张毅, 尚玫. Poisson theory and integration method for a dynamical system of relative motion[J]. 中国物理B, 2011, 20(2): 24501-024501.

Zhang Yi(张毅) and Shang Mei(尚玫) . Poisson theory and integration method for a dynamical system of relative motion[J]. Chin. Phys. B, 2011, 20(2): 24501-024501.

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Poisson theory and integration method for a dynamical system of relative motion

Poisson theory and integration method for a dynamical system of relative motion

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