This paper is intended to apply the potential integration method to the differential equations of the Birkhoffian system. The method is that, for a given Birkhoffian system, its differential equations are first rewrit...This paper is intended to apply the potential integration method to the differential equations of the Birkhoffian system. The method is that, for a given Birkhoffian system, its differential equations are first rewritten as 2n first-order differential equations. Secondly, the corresponding partial differential equations are obtained by potential integration method and the solution is expressed as a complete integral. Finally, the integral of the system is obtained.展开更多
This paper is intended to apply a potential method of integration to solving the equations of holonomic and nonholonomic systems. For a holonomic system, the differential equations of motion can be written as a system...This paper is intended to apply a potential method of integration to solving the equations of holonomic and nonholonomic systems. For a holonomic system, the differential equations of motion can be written as a system of differential equations of first order and its fundamental partial differential equation is solved by using the potential method of integration. For a nonholonomic system, the equations of the corresponding holonomic system are solved by using the method and then the restriction of the nonholonomic constraints on the initial conditions of motion is added.展开更多
The purpose of this paper is to study the solution of the celebrated Whittaker equations by using analytical mechanics methods, including the Lagrange-Noether method, Hamilton-Poisson method and potential integral met...The purpose of this paper is to study the solution of the celebrated Whittaker equations by using analytical mechanics methods, including the Lagrange-Noether method, Hamilton-Poisson method and potential integral method.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant Nos 10572021 and 10772025)
文摘This paper is intended to apply the potential integration method to the differential equations of the Birkhoffian system. The method is that, for a given Birkhoffian system, its differential equations are first rewritten as 2n first-order differential equations. Secondly, the corresponding partial differential equations are obtained by potential integration method and the solution is expressed as a complete integral. Finally, the integral of the system is obtained.
基金Project supported by the National Natural Science Foundation of China （Grant Nos 10272021 and 10572021 and the Doctoral Program Foundation of Institutions of Higher Education of China （Grant No 20040007022）.
文摘This paper is intended to apply a potential method of integration to solving the equations of holonomic and nonholonomic systems. For a holonomic system, the differential equations of motion can be written as a system of differential equations of first order and its fundamental partial differential equation is solved by using the potential method of integration. For a nonholonomic system, the equations of the corresponding holonomic system are solved by using the method and then the restriction of the nonholonomic constraints on the initial conditions of motion is added.
基金Project supported by the National Natural Science Foundation （Grant No 10572021） and the Doctoral Program Foundation of Institution of Higher Education of China （Grant No 20040007022）.
文摘The purpose of this paper is to study the solution of the celebrated Whittaker equations by using analytical mechanics methods, including the Lagrange-Noether method, Hamilton-Poisson method and potential integral method.
