Chain of Physically Related Independent Mechanical Oscillators
A. D. Sergeev
Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, St. Petersburg, 199178, Russia
Keywords: цепочки твердых тел, гипотеза Эйнштейна, chains of rigid bodies, Einstein's hypothesis
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.
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