非完整系统Boltzmann-Hamel方程的Birkhoff化及其广义辛算法  

The Borkhoffian expression of Boltzmann-Hamel equation of nonholonomic system and its generalized symplectic geometric algorithm

作　　者：解加芳[1] 庞硕[1] 邹杰涛[1] 李国富[1] 

机构地区：[1]北方工业大学理学院,北京100144

出　　处：《物理学报》2012年第23期1-5,共5页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:11102001;11026090)资助的课题~~

摘　　要：针对非完整系统的Boltzmann-Hamel方程,当其满足一定条件时,可以进行广义Birkhoff化.构造生成函数,利用当前比较优越的非自治Birkhoff广义辛算法对其进行数值仿真.仿真结果和传统的Runge-Kutta算法结果相比较,非自治Birkhoff广义辛算法在长期跟踪后更加准确.For a Boltzmann-Hamel equation of nonholonomic mechanical system, when it meets certain conditions, the Boltzmann-Hamel equation can be transformed into a Birkhoffian system. By constructing the generating function, the system is investigated numerically using the generalized symplectic geometric algorithm of the nonautonomous Birkhoffian system. Compared with the above-mentioned algorithm with the classical Runge-Kutta method, Birkhoffian symplectic scheme is very accurate in a long-term tracing.

关 键 词：非完整约束 Boltzmann—Hamel方程 Birkhoff辛算法 

分 类 号：O241.6[理学—计算数学]