The Violation Correction Null Space Method Of Dynamical Equation Of Flexible Multi-body Systems

Modeling and numerical solutions are the dynamics of flexible multibody systems'kernel contents.Many system control problem can be described with Differential Algebraic Equations, and the numerical solutions of the differential-algebraic equations have been the study spotlight and difficult problem in recent years.In this paper, we mainly described and studied the numerical solutions methods. Firstly, various numerical methods for dynamics of flexible multibody systems are discussed based on the the dynamics of flexible multibody systems theory, the advantages and disadvantages, applied range of those methods are analyzed. Several condensed methods are inturduced, which are based on the generalized coordinate independent decomposition in detail. Given the uses of all the matrix factorization methods in differential-algebraic equations and the null space method.Secondly, combine the advantage of the condensed method with constraint violation correction, We raised a new method, called a null space method of constraint violation correction. This method use a simple method to get the null space, separated independent coordinate, transform the differential-algebraic equations into ordinary differential equations,.At each time step, the initial iterative values were evaluated by Newmark-βmethod, when get the values, take them to the constraint violation correction formula, judge the displacements are constraint violation or not , modify the displacements, so that it can meet the displacements control equations of multibody systems. Finally, the stability and efficiency of the presented method are illustrated by the simulation results of one typical example.