according to wikipedia
https://en.wikipedia.org/wiki/Lagrange,_Euler,_and_Kovalevskaya_tops

The Euler top describes a free top without any particular symmetry, moving in the absence of any external torque in which the fixed point is the center of gravity. The Lagrange top is a symmetric top, in which two moments of inertia are the same and the center of gravity lies on the symmetry axis. The Kovalevskaya top[3][4] is a special symmetric top with a unique ratio of the moments of inertia which satisfy the relation

    I 1 = I 2 = 2 I 3 , {\displaystyle I_{1}=I_{2}=2I_{3},} {\displaystyle I_{1}=I_{2}=2I_{3},}

That is, two moments of inertia are equal, the third is half as large, and the center of gravity is located in the plane perpendicular to the symmetry axis (parallel to the plane of the two equal points). The nonholonomic Goryachev–Chaplygin top (introduced by D. Goryachev in 1900[5] and integrated by Sergey Chaplygin in 1948[6][7]) is also integrable ( I 1 = I 2 = 4 I 3 {\displaystyle I_{1}=I_{2}=4I_{3}} {\displaystyle I_{1}=I_{2}=4I_{3}}). Its center of gravity lies in the equatorial plane.[8] It has been proven that no other holonomic integrable tops exist .[9]

第4种是Goryachev–Chaplygin top，今天又涨了各种奇怪的知识@@
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修改:vinbo FROM 203.218.129.*
FROM 203.218.129.*
附件(812.5KB) The_Goryachev-Chaplygin_Top_and_the_Toda_Lattice(1987).pdf