多体系统动力学控制方程的精细时程积分法

Precise time integration algorithms of control equations on multibody system.dynamics are discussed. Using N 2 precise algorithms and the integration forms of.matrix function, numerical integration algorithms of stiff ordinary differential.equations are presented. The compatibility, convergence theorems, stability and error bounds involved in them are discussed. The integration methods not only have the explicit integral schemes, but also have the absolute stability and high accuracy,.which can avoid computational fatalness of stiff equations. Numerical examples show.that the precise integration algorithms are effective to solve stiff equations and.dynamic equations of multibody flexible systems. Based on Picard integral algorithm and information pick technology, the rule of information transmission is found and a information integral algorithm suitable for nonlinear autonomous dynamic systems can be obtained, which have special self-correction characteristics, high accuracy and absolute stability. The numerical example shows the algorithms are correct and effective, which may use a bigger step not to obtain higher precise nonlinear solution,but also to solve stiff nonlinear equations. Moreover, by discussing the information transmission form of differential equation, we have got something about the determinate motion, bifurcation and chaos of nonlinear maps.

研究多体系统动力学控制方程的数学结构和计算方法，将精细时程积分法拓展到非线性领域，探讨解决多体系统中柔性构件时变非线性刚弹耦合作用造成的数值计算刚性问题的方法，建立适合于数值求解多体系统高精度、高效率、强稳定性的显式精细时程积分法，为多体系统动力学计算理论的发展和工程应用作出努力。.