Kovalevskaya Top

In classical mechanics, the rotation of a rigid body such as a spinning top under the influence of gravity is not, in general, an integrable problem. There are however three famous cases that are integrable, the Euler, the Lagrange, and the Kovalevskaya top, which are in fact the only integrable cases when the system is subject to holonomic constraints.

In addition to the energy, each of these tops involves two additional constants of motion that give rise to the integrability.