효율적인 실시간 차량 시뮬레이션을 위한 자코비안 갱신이 불필요한 뉴턴 적분방법

Abstract

While implicit integration methods such as Newton's method have excellentstability for the analysis of stiff and constrained mechanical systems, they have thedrawback that the evaluation and LU‐factorization of the system Jacobian matrixrequired at every time step are time‐consuming. This paper proposes a Jacobianupdate‐free Newton's method in order to overcome these defects. Because themotions of all bodies in a vehicle model are limited with respect to the chassisbody, the equations are formulated with respect to the moving chassis‐bodyreference frame instead of the fixed inertial reference frame. This makes thesystem Jacobian remain nearly constant, and thus allows the Newton's method tobe free from the Jacobian update. Consequently, the proposed methodsignificantly decreases the computational cost of the vehicle dynamic simulation. This paper provides detailed generalized formulation procedures for the equationsof motion, constraint equations, and generalized forces of the proposed method.