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A Continuation. The Mandelstam-Andronov School

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Book cover Leonid Isaakovich Mandelstam

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Abstract

In this chapter an attempt is made to follow the further development of research which started by Andronov and Vitt under the guidance of Mandelstam in the second half of the 1920s and in the 1930s. In this connection the term “Mandelstam-Andronov school” is discussed and a comparison of Mandelstam-Andronov’s theory of nonlinear oscillations with Krylov-Bogoliubov’s non-linear mechanics is undertaken.

By appealing to the modern philosophy of science the author uses the concepts of paradigm and ideology to discuss the methodology of Andronov’s students (and their students) applied in their research in the physics of distributed systems.

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Notes

  1. 1.

    According to Th. Kuhn, a paradigm is characterized by (1) “symbolic generalizations”—differential equations which are basic in the area under discussion, (2) “ontological scheme” (the model of physical reality), (3) values, (4) “shared examples”. It was symptomatic that the tendency appeared to treat the concept of self-oscillations ideologically that is to say purely qualitatively as a set of rough pictorial schemes. For example, in A.A. Charkevich’s book [73] only the first 30 pages are dedicated to a rather mathematical discussion of self-oscillations. The rest is dedicated to a qualitative description of self-oscillations in many engines and phenomena.

  2. 2.

    Neymark’s contribution is represented in the books [68, 222, 223, 228, 230].

  3. 3.

    As one can read in his and Trubetskov’s 1984 book, “stochastic self-oscillations are random contingent motions which are powered in a dissipative system by a non-stochastic energy source” [268, p. 368].

  4. 4.

    The CL circuit is called a lumped system since capacity and inductance are localized in some points of it as mass in mechanical pendulum.

  5. 5.

    The Lecher system is two parallel wires along which electromagnetic waves propagate.

  6. 6.

    Mikhail Mikhailovich Shemiakin (1908–1970) became a great figure in Soviet organic chemistry. After his name Institute of Bioorganic Chemistry of the Academy of Sciences is called.

  7. 7.

    Sergei Pavlovich Strelkov (1905–1974) worked for Central Aerohydrodynamic Institute (TsAGI) and was Professor at MSU. He is the author of a popular textbook [301].

  8. 8.

    In Soviet scientific and especially in scientific popular and philosophical literature synergetics, which was introduced by Herman Haken as a theory of the parameters of order, is often taken as a very important research field which anticipates the future development of science. At that synergetics was treated as the general theory of self-organization (see, for example [178, 179, 317]).

  9. 9.

    As was noted above, Academician Andrei Victorovich Gaponov-Grekhov is a former Andronov’s student, Professor Mikhail Izrailievich Rabinovich is a former student of Gaponov-Grekhov.

  10. 10.

    [204] is referred to.

  11. 11.

    In connection with Neimark-Landa’s book Stokhasticheskiie i khaoticheskie kolebania “Stochastic and Chaotic Oscillations” [230] Y.I. Neimark said to the present author that this title should be read Stochastic and Chaotic Self-oscillations.

  12. 12.

    The position of Andronov’s school in the development of non-linear dynamics toward the theory of chaos is also outlined in [29, 79].

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  1. Department of Philosophy, Lomonosov Moscow State University, Moscow, Russia

    Alexander Pechenkin

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Pechenkin, A. (2014). A Continuation. The Mandelstam-Andronov School. In: Leonid Isaakovich Mandelstam. Springer, Cham. https://doi.org/10.1007/978-3-319-00572-0_10

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