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Euler and mathematical methods in mechanics (on the 300th anniversary of the birth of Leonhard Euler). (English. Russian original) Zbl 1140.01017
Russ. Math. Surv. 62, No. 4, 639-661 (2007); translation from Usp. Mat. Nauk 62, No. 4, 3-26 (2007).
This work is devoted to the creative work of the brilliant mathematician 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 nonlinear 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. A very brief description is also given about Euler’s life. The contributions by Euler is outstanding in physics, mathematics, solid mechanics and fluid mechanics.
The paper is very lucid and will be of interest to all researchers in the field of mechanics and mathematics.

MSC:
01A70 Biographies, obituaries, personalia, bibliographies
35Q05 Euler-Poisson-Darboux equations
35Q35 PDEs in connection with fluid mechanics
40G05 Cesàro, Euler, Nörlund and Hausdorff methods
70F15 Celestial mechanics
01A50 History of mathematics in the 18th century
70H20 Hamilton-Jacobi equations in mechanics
70-03 History of mechanics of particles and systems
Biographic References:
Euler, Leonhard
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