Violation of the invariance of the Euler–Lagrange equation

V. P. Koshcheev

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

Abstract: We showed that if, during the transition to a new coordinate system, the Jacobi determinant equals zero, so the invariance of the Euler–Lagrange equation is violated.

Keywords: Euler–Lagrange equation, Hamilton–Jacobi equation, Hamilton equation, differential forms, violation of invariance.