非Hamilton的Birkhoff系统的Noether守恒量的计算

Calculations on noether conserved quantities of the Non-Hamiltonian Birkhoffian system

利用辛几何的方法研究了非Hamilton的Birkhoff系统的Noether对称性与守恒量,揭示了非Hamilton的Birkhoff系统的Noether对称性与守恒量之间的关系,最后举例计算,为积分理论的研究提供了新的方法。

In this thesis, symplectic geometry is used to investigate the conserved quantities and symmetries of the Non-Hamiltonian Birkhoffian systems, hence the inner connection between the conserved quantities and the dynamical symmetries of the Non-Hamiltonian Birkhoffian system are revealed, at last,the corresponding Noether conserved quantities are deduced,which provides a new method to the study of integral theory.