Integrals of motion on extremals of the equation Euler-Lagrange
V. P. Koshcheev
TL;DR
This paper demonstrates that Wronsky determinants serve as integrals of motion on extremals of the Euler-Lagrange equation, linking the evolution of moments to the Jacobi equation.
Contribution
It introduces a method to construct a chain of closed systems of differential equations using the Jacobi equation, revealing new integrals of motion.
Findings
Wronsky determinants are integrals of motion on extremals.
A chain of closed systems for moments can be constructed via the Jacobi equation.
The approach connects the evolution of moments with the Euler-Lagrange extremals.
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.
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Taxonomy
TopicsAlgebraic and Geometric Analysis · Aerospace Engineering and Control Systems · Control and Dynamics of Mobile Robots