AUTOMATIC-GENERATION AND NUMERICAL-INTEGRATION OF DIFFERENTIAL-ALGEBRAIC EQUATIONS OF MULTIBODY DYNAMICS

An algorithm for computing the matrix and vector functions in the nume rical integration method of constrained equations of motion in multibo dy mechanical system dynamics is presented. Cartesian coordinates and Euler parameters have been used as the state variables to construct th e mathematical model for a spatial multibody mechanical system. Four b asic constraints, which describe the orthogonality and the parallelism of pairs of vectors, have also been written and will serve as buildin g blocks of the kinematic joint library. Derivatives of these basic co nstraints are then derived by applying differential operators to the m ultivariable and vector-valued constraint functions. Verification is d one by comparing the numerical solution with results computed by a sym bolic computation software. In multibody dynamics, the acceleration of constrained equations of motion is a function of the state variables. Using the differentials of joint library functions and generalized fo rce functions, the Jacobian of the acceleration with respect to the st ate variables is obtained. The efficiency and accuracy of computing th is analytic Jacobian matrix are demonstrated by comparing execution ti me and numerical results with those obtained by applying a first order linearization method. The proposed computational technique is also su itable for various formulations of the equations of motion, for instan ce, the Euler angles instead of the Euler parameters can be used for t he orientation variables. The final goal is to construct a standard li brary of joint constraints and force expressions for automatic generat ion of constrained equations of motion and to enhance the numerical in tegration methods for multibody dynamics.