The Pfaff-Birkhoff variational principle is discretized, and based on the discrete variational principle the discrete Birkhoffian equations are obtained. Taking the discrete equations as an algorithm, the correspondin...The Pfaff-Birkhoff variational principle is discretized, and based on the discrete variational principle the discrete Birkhoffian equations are obtained. Taking the discrete equations as an algorithm, the corresponding discrete flow is proved to be symplectic. That means the algorithm preserves the symplectic structure of Birkhofflan systems. Finally, simulation results of the given example indicate that structure-preserving algorithms have great advantage in stability and energy conserving.展开更多
基金Supported by the National Natural Science Foundation of China (10932002,10972031)
文摘The Pfaff-Birkhoff variational principle is discretized, and based on the discrete variational principle the discrete Birkhoffian equations are obtained. Taking the discrete equations as an algorithm, the corresponding discrete flow is proved to be symplectic. That means the algorithm preserves the symplectic structure of Birkhofflan systems. Finally, simulation results of the given example indicate that structure-preserving algorithms have great advantage in stability and energy conserving.
