N. A. Vinokurov, “Relation between energy conservation and equations of motion (a reply to the comment by E A Arinshtein [Phys. Usp. 58 309 (2015); Usp. Fiz. Nauk 185 333 (2015)] on “Analytical mechanics and field theory: derivation of equations from energy conservation” [Phys. Usp. 57 593 (2014); Usp. Fiz. Nauk 184 641 (2014)])”, UFN, 2015, Volume 185, Number 3,Pages 335

LETTERS TO THE EDITORS

Relation between energy conservation and equations of motion (a reply to the comment by E A Arinshtein [Phys. Usp. 58 309 (2015); Usp. Fiz. Nauk 185 333 (2015)] on “Analytical mechanics and field theory: derivation of equations from energy conservation” [Phys. Usp. 57 593 (2014); Usp. Fiz. Nauk 184 641 (2014)])

N. A. Vinokurov^ab

^a Budker Institute of Nuclear Physics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
^b Korea Atomic Energy Research Institute, Yuseong-gu, Daejeon

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

PACS: 45.20.-d, 45.20.Jj, 45.20.dh, 45.50.-j

Received: October 23, 2014
Accepted: October 29, 2014

DOI: 10.3367/UFNr.0185.201503g.0335