Symbolic linearization of differential/algebraic equation for multi-body system based on fully cartesian coordinates

The dynamics of a multi-body system can be described by 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 multi-body systems with small displacements efficiently, a computerized algebraic method for linearizing the equations of multi-body systems is discussed. Based on the fully Cartesian coordinates, a differential/algebraic equation system of multi-body 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.