Numerical Integration for DAEs of Multibody System Dynamics.docVIP

Numerical Integration for DAEs of Multibody System Dynamics 　　【Abstract】During the simulation of constrained multibody system， numerical integration is important for solving the Euler-Lagrange equation of multibody system dynamics， which is usually a Differential-Algebraic Equations （DAEs）. Using the discrete Hamilton principle， discrete Euler-Lagrangian equation is obtained first based on Lagrange Interpolation. Then the Romberg， Gauss integral is used to solve the DAEs. At last，numerical results are compared by using Euler method， Runge-Kutta method， Romberg method and Gauss method for a double pendulum system. 　　【Key words】Numerical integration； Multibody system dynamics； DAEs； Discrete euler-lagrange equation 　　0 Introduction 　　Multibody system[1-2] is connected multiple objects （rigid body and elastomer /soft body， particle， etc.） of system in a certain way. In weapons， robots， aviation， machinery and so on national defense and national economic construction， such as， aircraft launch system， robot， vehicle， such as large civil machinery mechanical system can be attributed to body systems. As the national economy and national defense construction to improve the mechanical system dynamic performance requirements， need for large complex mechanical system dynamics analysis and forecast accurately and quickly. 　　There are two ways to solve the differential algebraic equations. One is the direct integral method， combines acceleration constraint equation and dynamic equation of integral. Another way is condensed and method， by using the equation of the matrix decomposition independent coordinate system consists of a set of appropriate generalized coordinates， to pure differential equations， differential algebraic equation can be converted to then integral. Commonly used direct integral method has the Euler method and Runge-Kutta method， there are some higher order numerical integral method， such as Newton - Romberg integral and Gauss integral[4]， etc. 　　Hig