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Constructing the Euler–Lagrange equation using the Poincaré lemma

V. P. Koshcheev

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

Abstract: We demonstrate that the Euler–Lagrange equation for a dynamical system with one degree of freedom can be derived using the Poincaré lemma. In the appendix, we prove the theorem on the existence and uniqueness of the skew-symmetry property of the simplest (basic) differential forms.

Keywords: Euler–Lagrange equation, 1-DOF dynamic system, Poincaré lemma, simplest (basic) differential forms.