SYMBOLIC LINEARIZATION OF DIFFERENTIAL/ALGEBRAIC EQUATION FOR MULTIBODY SYSTEM BASED ON FULLY CARTESIAN COORDINATES

The dynamics of a multibody system can be described using either a differential equation system or a differential/algebraic equation system, both being for the systems with large displacements and strong nonlinearity. To study vibration systems or the multibody systems with small displacements efficiently, a computerized algebraic method for linearizing the equations of multibody system is discussed in this paper. Based on the fully Cartesian coordinates, a differential/algebraic equation system of multibody system dynamics is obtained. A successive linearization technique together with a computerized algebraic method is used to simplify the model symbolically. Taylor series expansions of the generalized mass matrix, the constraint equations and the generalized force matrix of the equation system are obtained respectively in the neighboring regions of their equilibrium positions by using the symbolic linearization technique, so that the system can be dealt with in a simple and efficient way and some drawbacks of numerical perturbation methods are avoided. Two examples are given to show the effectiveness and correctness of the method.