Computer simulation of spherical motion of solid bodies

Abstract

The article discusses the computer simulation of the rotation of solid bodies around a fixed point, in which a moving body is replaced by a system of material points connected by weightless viscoelastic rods. A computer program calculates the distance between particles at the initial moment of time and stores it in an matrix. In the course of the movement, the elastic forces acting between the particles, the viscous friction forces arising from the relative motion of the particles, and the gravity forces are taken into account. To integrate the equations of motion, the Euler method is used; at this the acceleration, velocity and coordinates of the particles at the next point of time is calculated. The precession of symmetric and asymmetric gyroscopes in the gravity field, as well as unstable rotation of the body around an intermediate inertia axis are considered. Two programs written in the Free Pascal IDE are presented; the simulation results (the movement trajectories of various points of a rotating body projected on coordinate planes, as well as graphs of changes of the precession and nutation angles over time) are analyzed. It is shown that at free rotation around the intermediate axis, the body having made several turns makes a roll, turning on 180 degrees and continues to rotate so that its angular momentum does not change.