This paper presents a computer-based method for finding static equilibrium position, for constructing equations of motion, and for time domain dynamic analysis of a vehicle modeled as a three dimensional multibody system composed of rigid bodies, joints, spring and dampers. A mixed set of generalized coordinates with three translational and three rational coordinates for each rigid body in the system is used to specify the position of the system. Here three translational coordinates are the cartesian coordinates of absolute coordinate system and three rotational coordinates are Euler angles in xyz convention so that each of the angles represents yawing, rolling and pitching respectively.
Minimum potential energy principle and gradient projection method are utilized to find static equilibrium position, and constraint violation stabilization method is used to solve differential algebraic equation formed by coupling the equations of motion with constraint equations through Lagrange multiplier technique.
A method to determine the optimal feedback coefficients for the constraints violation stabilization method by minimizing the constraint violation propagation is presented. The constraint violation propagation is derived from a stability analysis on the error propagation dynamics for the dynamic for the dynamic equations of constraint which is discretized by Runge-Kutta method in discrete domain.
Several examples are given to illustrate the applicability of the VEDA (Vehicle Dynamic Analysis) program and to show the effectiveness of proposed method to determine the feedback coefficients.
