Has the Problem of the Motion of a Heavy Symmetric Top Been Solved in Quadratures?

Abstract

We have revised the problem of the motion of a heavy symmetric top. When formulating equations of motion of the Lagrange top with the diagonal inertia tensor, the potential energy has more complicated form as compared with that assumed in the literature on dynamics of a rigid body. Using the Liouville's theorem, we solve the improved equations in quadratures and present the explicit expressions for the resulting elliptic integrals.

Tetama nas matas mineiras: sítios Tupi na microrregião de Juiz de Fora - MG

“…The traditional way is to solve the equations ( 2) and (3) by rewriting them through the Euler angles, and in the Laboratory frame with a third axis directed along the vector of conserved angular momentum [5]. Some specific features of rigid body dynamics, that must be taken into account within this method, are discussed in recent works [7,8].…”