Integrable tops

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Last updated: March 22, 2025

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Hint	Answer
A free top without any particular symmetry moving in the absence of any external torque	Euler
A symmetric top, in which two moments of inertia are the same and the center of gravity lies on the symmetry axis	Lagrange
A special symmetric top with a unique ratio of the moments of inertia which satisfy the relation I1=I2=2 * I3 and a center of mass that lies in the plane perpendicular to the symmetry axis	Kovalevskaya
A nonholonomic top in which I1 = I2 = 4 * I3	Goryachev–Chaplygin