Euler and mathematical methods in mechanics (on the 300th anniversary of the birth of Leonhard Euler)

摘要

This article concerns the life of Leonhard Euler and his achievements in theoretical mechanics. A number of topics are discussed related to the development of Euler's ideas and methods: divergent series and asymptotics of solutions of non-linear differential equations; the hydrodynamics of a perfect fluid and Hamiltonian systems; vortex theory for systems on Lie groups with left-invariant kinetic energy; energy criteria of stability; Euler's problem of two gravitating centres in curved spaces.