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Applied aspects of the theory of adiabatic invariants

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Abstract

We consider the applicability of the theory of adiabatic invariants to determining the reaction of a linear oscillator that simulates the inverse problem of measurement technology taking account of the dynamics of a sensing element. An indication is given of the applicability of the ideas and methods developed in the papers of Ya. S. Podstrigach and his school to the solution of this circle of problems.

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Literature cited

  1. V. I. Arnol'd, “Small denominators and the problem of stability of motion in classical and celestial mechanics,”Usp. Mat. Nauk,18, 91–142 (1963).

    Google Scholar 

  2. A. S. Bakai, “Asymptotic methods in theoretical physics” in:Problems of the Asymptotic Theory of Nonlinear Vibrations [in Russian], Naukova Dumka, Kiev (1977), pp. 17–42.

    Google Scholar 

  3. A. S. Bakai and Yu. P. Stepanovskii,Adiabatic Invariants [in Russian], Naukova Dumka, Kiev (1981).

    Google Scholar 

  4. N. N. Bogolyubov,On Certain Statistical Methods in Mathematical Physics [in Russian], Academy of Sciences of the USSR, L'vov (1945).

    Google Scholar 

  5. N. N. Bogolyubov and Yu. A. Mitropol'skii, “The method of integral varieties in nonlinear mechanics,” in:Proceedings of the International Symposium on Nonlinear Vibrations [in Russian], Ukrainian Academy of Sciences Press, Kiev (1963), Vol. 1, pp. 93–154.

    Google Scholar 

  6. L. Boltzmann, “Two excerpts from ‘Lectures on the Principles of Mechanics’,” in:Variational Principles of Mechanics [in Russian], Fizmatgiz, Moscow (1959), pp. 466–496.

    Google Scholar 

  7. V. V. Brostyuk, M. I. Kiselev, and V. A. Kuzivanov, “On the possibility of applying high-quality seismometers,”Dokl. Akad. Nauk SSSR,265, No. 5, 1097–1100 (1982).

    Google Scholar 

  8. A. Sommerfeld,Structure of Atoms and Spectra [Russian translation], Vol. 1, Gostekhizdat, Moscow (1956).

    Google Scholar 

  9. M. I. Kiselev and V. A. Kuzivanov, “On the possibility of measurements in geophysics by weakly damped systems,”Dokl. Akad. Nauk SSSR,253, No. 4, 853–856 (1980).

    Google Scholar 

  10. A. N. Kolmogorov, “On the preservation of conditionally-periodic motions under a small change in the Hamiltonian function,”Dokl. Akad. Nauk SSSR,98, No. 4, 527–530 (1954).

    Google Scholar 

  11. M. Kruskal, Adiabatic Invariants [Russian translation], Izdatel'stvo Inostrannoi Literatury, Moscow (1962).

    Google Scholar 

  12. Yu. A. Krutkov, “Adiabatic invariants and their application in theoretical physics,”Zh. Rus. Fiz.-Khim. Obshch,53, No. 1, 83–91 (1921).

    Google Scholar 

  13. A. N. Tikhonov and V. Ya. Arsenin,Methods of Solving Ill-posed Problems [in Russian], Nauka, Moscow (1986).

    Google Scholar 

  14. P. Ehrenfest, “On a mechanical theorem of Boltzmann and its relation to quantum theory,” in:Relativity. Quantum Theory. Statistics [in Russian], Nauka, Moscow (1972), pp. 51–57.

    Google Scholar 

  15. N. Bohr, “On the quantum theory of line spectra,” Copenhagen (1918).

  16. R. Clausius, “Über die Zurückführung des zweiten Hauptsatzes der Wärmetheorie auf allgemeine mechanische Prinzipen,”Pogg. Ann.,142 (1871);146 (1872).

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Authors
  1. M. I. Kiselev
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Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 35, 1992, pp. 163–167.

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Kiselev, M.I. Applied aspects of the theory of adiabatic invariants. J Math Sci 67, 2976–2979 (1993). https://doi.org/10.1007/BF01095881

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