Abstract
The term “Mandelstam-Andronov school” is not so widespread as the term “Mandelstam school” which has been in the center of our discussion till now. However, the term “Mandelstam-Andronov school” is present in the literature. The former Andronov’s graduate student Y.I. Neymark, who considers himself to be a representative of the Mandelstam-Andronov school, used this term by emphasizing the conceptual contribution of A.A. Andronov to the theory of oscillations and his organizational role in the formation of physics in Nizhny Novgorod (in the Soviet Union this city was named Gorky). Neymark also emphasized Andronov’s high moral standards, which corresponded to the moral standards of Mandelstam and his disciples but appearing in a new situation—in the situation of provincial science.
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Notes
- 1.
According to Th. Kuhn, the paradigm (the disciplinary matrix) 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 [77] 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.
Neymark’s contribution is represented in the books [245, 246, 248, 253]. Neymark wrote about A.A. Andronov and his school in [248, 250, 252].
- 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” [345, p. 368].
- 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.
The Lecher system is two parallel wires along which electromagnetic waves propagate.
- 6.
Fedor Mikhailovich Shemiakin was a specialist in analytical chemistry (see: Pechenkin A. The history of research on chemical periodic processes. Springer. 2018).
- 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 [329].
- 8.
In Russian scientific and especially in scientific popular and philosophical literature synergetics, which was introduced by Herman Haken as a theory of the parameters of order, was often taken as a very important research field which anticipates the future development of science. Synergetics is treated as the general theory of self-organization.
- 9.
As was noted above, Academician Andrei Victorovich Gaponov-Grekhov is a former Andronov’s student, Professor Mikhail Izraiilievich Rabinovich is a former student of Gaponov-Grekhov.
- 10.
Rabinovich referred to [227].
- 11.
In connection with Neymark-Landa’s book Stokhasticheskiie i khaoticheskie kolebania “Stochastic and Chaotic Oscillations” [253] Y.I. Neymark said to the present author that this title should be read Stochastic and Chaotic Self-oscillations.
- 12.
The position of Andronov’s school in the development of non-linear dynamics toward the theory of chaos is also outlined in [31, 84, 85].
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Pechenkin, A. (2019). A Continuation—The Mandelstam-Andronov School. In: L.I. Mandelstam and His School in Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-17685-3_10
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