Relation between energy conservation and equations of motion (A reply to the comment by E A Arinshtein (Usp. Fiz. Nauk 185 333 (2015) [Phys. Usp. 58 (3) (2015)]) on "Analytical mechanics and field theory: derivation of equations from energy conservation" (Usp. Fiz. Nauk 184 641 (2014) [Phys. Usp. 57 593 (2014)]))

N.A. Vinokurov^a, b, c
^aBudker Institute of Nuclear Physics, Siberian Branch of the Russian Academy of Sciences, prosp. akad. Lavrenteva 11, Novosibirsk, 630090, Russian Federation
^bKorea Atomic Energy Research Institute, Daedeok-Daero, Yuseong-gu, Daejeon, 305-353, Republic of Korea
^cNovosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russian Federation

Equations of motion that conserve a given function (called energy) of generalized coordinates and velocities are derived. These equations differ from Lagrange's ones by presence of additional terms describing generalized gyroscopic forces. The relation between energy conservation and d'Alembert's principle is noted.

PACS: 45.20.−d, 45.20.Jj, 45.20.dh, 45.50.−j (all)
DOI: 10.3367/UFNe.0185.201503g.0335
URL: https://ufn.ru/en/articles/2015/3/f/
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000356096100006
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2015PhyU...58..311V
Citation: Vinokurov N A "Relation between energy conservation and equations of motion (A reply to the comment by E A Arinshtein (Usp. Fiz. Nauk 185 333 (2015) [Phys. Usp. 58 (3) (2015)]) on "Analytical mechanics and field theory: derivation of equations from energy conservation" (Usp. Fiz. Nauk 184 641 (2014) [Phys. Usp. 57 593 (2014)]))" Phys. Usp. 58 311–312 (2015)

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Received: 23rd, October 2014, accepted: 29th, October 2014

Оригинал: Винокуров Н А «Связь закона сохранения энергии и уравнений движения (Ответ на комментарий Э.А. Аринштейна [УФН 185 ЗЗЗ (2015)] к статье "Вывод уравнений аналитической механики и теории поля из закона сохранения энергии" [УФН 184 641 (2014)])» УФН 185 335–336 (2015); DOI: 10.3367/UFNr.0185.201503g.0335