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Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2018, Volume 59, Issue 5, Pages 178–184
DOI: https://doi.org/10.15372/PMTF20180520
(Mi pmtf537)
 

Chain of physically related independent mechanical oscillators

A. D. Sergeev

Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, St. Petersburg, 199178, Russia
Abstract: A lumped-parameter mechanical system consisting of a chain of physically related solids, each of which has one rotational degree of freedom. It is shown that inertial-free elastic elements that connect absolutely rigid bodies of the chain can be chosen in such a way that the mechanical structure acquires the properties of the so-called absolute mechanical filter. The motion of any inertial element of this system is described by the equation of a classical harmonic oscillator with one degree of freedom. Using the system considered as an example, it is shown that there is a relationship between the models of classical and quantum mechanics. From the positions of modern classical mechanics, this lumped-parameter system confirms the Einstein's hypothesis well-known in theoretical physics and stating that a solid is a system of independent oscillators.
Keywords: chains of rigid bodies, Einstein's hypothesis.
Received: 01.02.2018
Revised: 26.03.2018
English version:
Journal of Applied Mechanics and Technical Physics, 2018, Volume 59, Issue 5, Pages 922–927
DOI: https://doi.org/10.1134/S0021894418050206
Bibliographic databases:
Document Type: Article
UDC: 534
Language: Russian
Citation: A. D. Sergeev, “Chain of physically related independent mechanical oscillators”, Prikl. Mekh. Tekh. Fiz., 59:5 (2018), 178–184; J. Appl. Mech. Tech. Phys., 59:5 (2018), 922–927
Citation in format AMSBIB
\Bibitem{Ser18}
\by A.~D.~Sergeev
\paper Chain of physically related independent mechanical oscillators
\jour Prikl. Mekh. Tekh. Fiz.
\yr 2018
\vol 59
\issue 5
\pages 178--184
\mathnet{http://mi.mathnet.ru/pmtf537}
\crossref{https://doi.org/10.15372/PMTF20180520}
\elib{https://elibrary.ru/item.asp?id=35606614}
\transl
\jour J. Appl. Mech. Tech. Phys.
\yr 2018
\vol 59
\issue 5
\pages 922--927
\crossref{https://doi.org/10.1134/S0021894418050206}
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