The problem of rotation of a rigid body around a fixed point and the tautochrone problem in Somov fundamental research

The talk will present a study of the solution of model problems of mechanics on the example of the problem of rotation of a rigid body around a fixed point and the problem of tautochrone. We will consider the following stages: formulation and solution of these problems by Leonhard Euler; practical analytical advancement of problems by Joseph Louis Lagrange; development of mathematical methods for solving the presented problems in the works of Niels Abel and Carl Jacobi. General analytical solutions of these problems lead to integral equations, hyperelliptic functions and field theory. We will talk about the fundamental research of the mid-19th century by Osip Ivanovich Somov, where he innovatively used the theory of elliptic functions and elements of field theory in applications to these problems of mechanics.
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