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JOURNALS // Prikladnaya Mekhanika i Tekhnicheskaya Fizika // Archive

Prikl. Mekh. Tekh. Fiz., 2018 Volume 59, Issue 5, Pages 178–184 (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.

UDC: 534

Received: 01.02.2018
Revised: 26.03.2018

DOI: 10.15372/PMTF20180520


 English version:
Journal of Applied Mechanics and Technical Physics, 2018, 59:5, 922–927

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© Steklov Math. Inst. of RAS, 2024