Integrals of motion on extremals of the equation Euler-Lagrange

arXiv:2508.11735v1 Announce Type: new
Abstract: It is 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. It is shown that Wronsky determinants for fundamental matrices of closed systems of first order ordinary differential equations are integrals of motion on extremals of the Euler-Lagrange equation.