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This study proposes a combined method of the multi-body system theory and the Jourdain’s principle to study the automotive vibration. A 3D dynamic model of the automotive is built based on the multi-body system theory, the vibration equations are described based on two methods including a method of the Jourdain’s principle and the traditional method of the Newton-Euler’s principle. Matlab/Simulink software is used to solve the vibration equations under the excitation of the step road. The results show that the acceleration responses of the vertical, pitch and roll vibrations of the vehicle’s body with the Jourdain’s method are similarly in comparison with the traditional method. Therefore, the Jourdain’s method not only is applied for studying the kinetic and dynamic model of multi-body systems but also can be applied for studying the automotive vibration. Especially, nonlinear properties of objects in the vibration model can be clearly described by the Jourdain’s method via the recursive Jacobian matrices.

A modified technique for studying the automotive vibrations based on Jourdain’s principle