Revisiting the Spinning Top

This paper revisits the problem of a spinning top in a uniform gravitational field when one point on the symmetry axis is fixed in space. It is an instructive and synthetic work of which the theoretical part includes all necessary issues to formulate the full differential equations governing the general motion of the spinning top under arbitrary initial conditions. Both Euler and Lagrange formulations are discussed. Moreover, closed form analytical solutions are derived for the regular precession and the nutation. The numerical integration of the equations was achieved using the standard Runge-Kutta scheme ODE45 available in MATLAB®, which was initially applied to the totality of Euler’s equations and then to Lagrange’s equations. Also, in house RK2 and RK4 Runge-Kutta as well as Crank-Nicolson schemes were applied in conjunction with the constraint for energy conservation. The quality of the numerical solution was evaluated by testing the conservation of total energy as well as angular momenta in the form of residuals in the corresponding Euler’s dynamic equations.