中国物理B ›› 2014, Vol. 23 ›› Issue (6): 64501-064501.doi: 10.1088/1674-1056/23/6/064501
• ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS • 上一篇 下一篇
刘世兴a, 花巍b, 郭永新a
Liu Shi-Xing (刘世兴)a, Hua Wei (花巍)b, Guo Yong-Xin (郭永新)a
摘要: In this paper, we present a new integration algorithm based on the discrete Pfaff-Birkhoff principle for Birkhoffian systems. It is proved that the new algorithm can preserve the general symplectic geometric structures of Birkhoffian systems. A numerical experiment for a damping oscillator system is conducted. The result shows that the new algorithm can better simulate the energy dissipation than the R-K method, which illustrates that we can numerically solve the dynamical equations by the discrete variational method in a Birkhoffian framework for the systems with a general symplectic structure. Furthermore, it is demonstrated that the results of the numerical experiments are determined not by the constructing methods of Birkhoffian functions but by whether the numerical method can preserve the inherent nature of the dynamical system.
中图分类号: (Lagrangian and Hamiltonian mechanics)