Integrals of motion on the extrema of the Euler–Lagrange equation

V. P. Koshcheev

Moscow Aviation Institute (National Research University), Strela Branch, Zhukovsky, Moscow Region, Russian Federation

Abstract: It was previously shown that a chain of closed systems of first-order ordinary differential equations describing the evolution of moments can be constructed using the Jacobi equation. The Wronskians for the fundamental matrices of these closed systems are integrals of motion along the extremals of the Euler–Lagrange equation.

Keywords: Euler–Lagrange equation, Jacobi equation, chain of closed systems of ordinary differential equations of the first order, integrals of motion on extremals.