Simulation Of Multi - Body System Dynamics Based On Higher - Order Numerical Integral Method

Dynamic modeling and solving is the main content of multibody system dynamics simulation. Differential-algebraic equation is the normal multibody system dynamics model. The stability, efficiency and precision of the numerical integration are purposes of many research scholars in dynamics and applied mathematics area.The traditional method requires small numerical integration step size, for the larger step size, the simulation results highly divergent, severely limit the numerical integration step selection, and not suitable for long time simulation. In this paper,high-order numerical method is studied to solve these problems.High-order numerical integration method is based on discrete variational principle. On the discrete time intervals, the state variable function is interpolated.With high-precision numerical integration formula, the discrete Euler-Lagrange equation is gotten, and then solved for simulation.In this paper, the methods solving the multi-body system dynamics and classical mathematical model numerically are studied first. Then for differential-algebraic equations of multibody system dynamics, Lagrange interpolation is used to obtain the state variables interpolation function and its derivative interpolation function.Combined with Gauss integration, Romberg integration and other integration methods,high-order numerical integration methods for multibody system dynamics simulation are designed. Through double pendulum system and crank-slider system simulation,the errors of generalized coordinate, generalized speed, energy and constraints are analyzed and compared to verify the effectiveness of the high-order numerical integration method.