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Integrable tops

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Last updated: March 22, 2025
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First submittedMarch 2, 2025
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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
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