Stability of rigid body rotation from a bond graph perspective

This paper describes the history of the bond graph description of rigid body rotation dynamics and resolves a 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.