THE EXPLICIT GIBBS-APPELL EQUATIONS of MOTION for RIGID-BODY CONSTRAINED MECHANICAL SYSTEM

The present paper aims to provide a direct formulation for rigid body dynamics in terms of quasi-velocities. The general form of explicit equations of motion was provided for mechanical systems subjected to holonomic and nonholonomic constraints by using Gibbs-Appell method. The proposed method aimed to select quasi-velocities which satisfy all constraint conditions, eliminate the Lagrange multipliers, and reduce the number of equations. This method was used in the presence of both holonomic and nonholonomic constraints. Finally, the suggested approach was employed to derive the equations of motion for a rolling disk as an illustrative example and compare the results with Udwadia-Kalaba method.