Relative kinematics exploited in Kane's approach to describe multibody systems in relative motion

Abstract

Different from the usual use of Kane's approach a description of mechanical systems in relative motion is presented in the paper. Kane's equations require determination of the absolute motion of the system with regard to an inertial reference frame. If one wants to apply these equations to a system moving relative to a noninertial reference frame, one still needs to determine the absolute motion of the system by summing up to the motion of the moving reference frame and the system's motion relative to this frame. Results of the paper permit a direct formulation of the equations of motion without the need to determine the absolute motion. This is achieved by adaptation of Kane's equations to relative motion, which is general and may be applied to any mechanical system in relative motion. We obtained our results for purposes of railway vehicle dynamics. Hence some material concerning automatic generation of the equations of motion for the systems of a railway vehicle type is included as an example of the application of our approach.