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
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.
