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Euler and mathematical methods in mechanics. (English. Russian original) Zbl 1307.01009
Proc. Steklov Inst. Math. 272, Suppl. 2, S191-S207 (2011); translation from Sovrem. Probl. Mat. 11, 39-70 (2008).
While this paper contains brief descriptions concerning Euler and his work, the core of the paper is the presentation of aspects of his vast heritage. In particular, several topics associated with Euler are linked to modern work published in the last 30 years. For example, the section on divergent series and the Lagrange-Dirichlet theorem connects Euler’s summation work to a result of A. N. Kuznetsov in 1972. The paper reminds us that Euler developed the theory of motion of rotating bodies and the least-action principle. In hydrodynamics, Euler’s equations of motion for an ideal fluid lead to a description of stationary flow and the work of V. I. Arnold and the author on the hydrodynamics of Hamiltonian systems. A paper of the author from 1990 relates to vortex theory and Euler’s top. Mentioning Euler’s investigations of elasticity he introduces a synopsis of modern developments in stability theory of elastic systems. Finally, it is shown how Euler’s topic of two fixed centers of gravity has been generalized to any space of constant curvature. Altogether, the paper is a useful, even though brief, exposition of a large body of work.
MSC:
01A50 History of mathematics in the 18th century
01A65 Development of contemporary mathematics
01A70 Biographies, obituaries, personalia, bibliographies
70-03 History of mechanics of particles and systems
76-03 History of fluid mechanics
Biographic References:
Euler, Leonhard
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