Based on modern differential geometry, the symplectic structure of a Birkhoffian system which is an extension of conservative and nonconservative systems is analyzed. An integral invariant of Poincaré_Cartan...Based on modern differential geometry, the symplectic structure of a Birkhoffian system which is an extension of conservative and nonconservative systems is analyzed. An integral invariant of Poincaré_Cartan's type is constructed for Birkhoffian systems. Finally, one_dimensional damped vibration is taken as an illustrative example and an integral invariant of Poincaré's type is found.展开更多
The Lie symmetry is an invariance of the differential equations of motion under the infinitesimal transformations. The form invariance is an invariance of the form of the mechanical equations of motion under the infin...The Lie symmetry is an invariance of the differential equations of motion under the infinitesimal transformations. The form invariance is an invariance of the form of the mechanical equations of motion under the infinitesimal transformations. In this paper, the relation between form invariance and Lie symmetry of Birkhoffian systems is presented, and the relationship unveil that the form invariance does not always mean Lie symmetry, vice versa.展开更多
基金国家自然科学基金，国家自然科学基金，国家自然科学基金，Science Research Foundation of Liaoning Educational Committee of China
文摘Based on modern differential geometry, the symplectic structure of a Birkhoffian system which is an extension of conservative and nonconservative systems is analyzed. An integral invariant of Poincaré_Cartan's type is constructed for Birkhoffian systems. Finally, one_dimensional damped vibration is taken as an illustrative example and an integral invariant of Poincaré's type is found.
基金Supported by the Education Foundation of Anhui Province, China (No. 2004 kj294)
文摘The Lie symmetry is an invariance of the differential equations of motion under the infinitesimal transformations. The form invariance is an invariance of the form of the mechanical equations of motion under the infinitesimal transformations. In this paper, the relation between form invariance and Lie symmetry of Birkhoffian systems is presented, and the relationship unveil that the form invariance does not always mean Lie symmetry, vice versa.
