 Lagrange, Euler, and Kovalevskaya tops

The Lagrange, Euler, and Kovalevskaya tops are three integrable cases of fixed-point rigid body dynamics. The Euler top has no external torque; the Lagrange top has axial symmetry and its center of mass on the symmetry axis; the Kovalevskaya top has two equal principal moments twice the third and its center of mass in the corresponding principal plane.

The terms Lagrange top, Euler top, and Kovalevskaya top refer to specific types of rigid body dynamics problems in classical mechanics, particularly in the study of the motion of spinning tops. Each of these tops represents different cases of motion, characterized by their initial conditions, constraints, and governing equations. ### 1. Lagrange Top: The Lagrange top is a system characterized by a symmetric top that can move freely about a fixed point (like an axis).