This paper focuses on studying the Poisson theory and the integration method of a Birkhoffian system in the event space. The Birkhoff＇s equations in the event space are given. The Poisson theory of the Birkhoffian sy...This paper focuses on studying the Poisson theory and the integration method of a Birkhoffian system in the event space. The Birkhoff＇s equations in the event space are given. The Poisson theory of the Birkhoffian system in the event space is established. The definition of the Jacobi last multiplier of the system is given, and the relation between the Jacobi last multiplier and the first integrals of the system is discussed. The researches show that for a Birkhoffian system in the event space, whose configuration is determined by （2n ＋ 1） Birkhoff＇s variables, the solution of the system can be found by the Jacobi last multiplier if 2n first integrals are known. An example is given to illustrate the application of the results.展开更多
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...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.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.10972151)
文摘This paper focuses on studying the Poisson theory and the integration method of a Birkhoffian system in the event space. The Birkhoff＇s equations in the event space are given. The Poisson theory of the Birkhoffian system in the event space is established. The definition of the Jacobi last multiplier of the system is given, and the relation between the Jacobi last multiplier and the first integrals of the system is discussed. The researches show that for a Birkhoffian system in the event space, whose configuration is determined by （2n ＋ 1） Birkhoff＇s variables, the solution of the system can be found by the Jacobi last multiplier if 2n first integrals are known. An example is given to illustrate the application of the results.
基金supported by the National Natural Science Foundation of China (Grant No. 10972151)
文摘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.
