Conservative motion of a discrete, hexahedral gyroscope

Abstract

Gyroscopic motion is simulated by applying a molecular dynamics formulation to a rigid hexahedron. The mass is lumped at the vertices and the system is modeled as a collection of five particles subject to rigid body constraints. The conservative dynamical differential equations is solved numerically in such a fashion that all the system invariants are preserved. At each time step, a system of 30 nonlinear algebraic equations is solved to yield the positions and velocities of the five particles. Examples which included precession, nutation and a combination of looping and cusp formation are described and discussed.