Can we refer to Hamilton equations for an oscillator with friction?

A.G. Shalashov^a, b
^aFederal Research Center A.V. Gaponov-Grekhov Institute of Applied Physics of the Russian Academy of Sciences, ul. Ulyanova 46, Nizhny Novgorod, 603000, Russian Federation
^bLobachevsky State University of Nizhny Novgorod (National Research University), prosp. Gagarina 23, Nizhny Novgorod, 603950, Russian Federation

A formal possibility of describing a one-dimensional dissipative problem ẍ = f/(x, ẋ) with completely conservative Lagrange or Hamilton equations is discussed. A reference case of a harmonic oscillator with a linear friction is considered in detail.

Keywords: classical mechanics, Lagrange equations, Hamilton equations, energy integral, conservative and dissipative systems
PACS: 45.05.+x, 45.20.−d (all)
DOI: 10.3367/UFNe.2017.12.038273
URL: https://ufn.ru/en/articles/2018/11/e/
Web of Science

000457154900005
Scopus

2-s2.0-85062259593
ADS NASA

2018PhyU...61.1082S
Citation: Shalashov A G "Can we refer to Hamilton equations for an oscillator with friction?" Phys. Usp. 61 1082–1088 (2018)

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Received: 4th, September 2017, revised: 21st, December 2017, accepted: 26th, December 2017

Оригинал: Шалашов А Г «Можно ли говорить об уравнениях Гамильтона для осциллятора с трением?» УФН 188 1191–1197 (2018); DOI: 10.3367/UFNr.2017.12.038273