Kane’s Equations for Nonholonomic Systems in Bond-Graph-Compatible Velocity and Momentum Forms

Applied Dynamics International’s (ADI) Senior Applications Engineer, Mr. James R. Phillips, along with co-author, Dr. Farid Amirouche, presented this paper at the ECCOMAS Thematic Conference on Multibody Dynamics in December 2021. This paper is a continuation of a paper written in 2017, which can be found here. ADI congratulates Mr. James R. Phillips and Dr. Amirouche for this achievement.

The authors’ previously published results on a nonholonomic momentum form of Kane’s equations are extended from scleronomic to rheonomic systems. The momentum form is found to be partially Hamiltonian, and a new velocity form is found that is partially Lagrangian. The results are derived for general particle systems, and then specialized to rigid-body systems. Except for externally constrained velocities, all system matrices are independent of time, making the results power-conserving, and suitable for use with bond graphs. A new nonholonomic IC (NIC) bond-graph element is defined, and bond graphs for the new results are exhibited using this element.