On the history of the problem of a rigid body rotation around a fixed point in the case of an initial impact

The classical problem of a rigid body rotation dates back to L. Euler and J.L. Lagrange. Professor of St. Petersburg University Osip Ivanovich Somov used the apparatus of Jacobi elliptic functions to solve this problem. In 1850, Somov obtained a solution to this problem in the case of an initial impact by integrating the differential equations of motion with the help of Jacobi elliptic functions of the third kind with an imaginary parameter. His work connects both in time and logic of solving the problem of a rigid body rotation posed by Euler with the works of S.V. Kovalevskaya, and the theory of Jacobi elliptic functions with Weierstrass elliptic functions. By 1871 K. Weierstrass simplified the system of Jacobi elliptic functions, added hyperelliptic functions, and S.V. Kovalevskaya expanded the rigid body rotation problem around a fixed point, shifting the center of gravity of the body to an arbitrary position.

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