Conservative motion of a discrete, dodecahedral gyroscope. (Q1609468)

A discrete model of rigid body is suggested in the spirit of molecular mechanics as a dodecahedral body with mass particles on vertices. Based on this new approach, the motion of rigid body can be described by Newtonian mechanics without application of Eulerian angles, dyadics or other attitude parameters. The dynamic equations and a numerical method for their solution are presented, where the potential forces are introduced between two neighboring particles to assure the rigidity of the body. The parameter of the force is chosen to ensure that the attraction and repulsion occur over a very short period of time. Some numerical examples are given, and the trajectories of the tip of axis are illustrated for different cases.