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Analysis reveals that Wronsky determinants serve as integrals of motion in systems described by the Euler-Lagrange equation.
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.
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В. П. Кощеев (2025) studied this question.
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