Stability of rigid body rotation from a bond graph perspective

This paper describes file history of the bond graph description of rigid body rotation dynamics and resolves it paradox that resulted from the common Euler Junction Structure (EJS) description of the exterior product in the Newton-Euler equation describing rigid body rotation [D.C. Karnopp, R.C. Rosenberg, Analysis and Simulation of Multiport Systems - The Bond Graph Approach to Physical Systems Dynamics, MIT Press, Boston, 1968; D.C. Karnopp, The energetic structure of multibody dynamic systems, J. Franklin Inst. 306 (2) (1978) 165-181]. The proposed alternative representation that resolves this paradox allows direct insight into the stability of rotations around the principal axes of a rigid body. It eliminates the bond loop and it is shown to be a canonical decomposition of the corresponding nonlinear 3-port gyrator. whereas the EJS is not canonical. The consequences of these differences are demonstrated, in particular the increased expressive power of this notation, which is particularly important in education. (C) 2008 Elsevier B.V. All rights reserved.