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
a Budker Institute of Nuclear Physics, Siberian Branch of the Russian Academy of Sciences, prosp. akad. Lavrenteva 11, Novosibirsk, 630090, Russian Federation
b Korea Atomic Energy Research Institute, Daedeok-Daero, Yuseong-gu, Daejeon, 305-353, Republic of Korea
c Novosibirsk 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.