Commutator of C∞-symmetries and reduction of Euler–Lagrange equations
نویسندگان
چکیده
A novel procedure to reduce by four the order of Euler–Lagrange equations associated to n-th order variational problems involving single variable integrals is presented. In preparation, a new formula for the commutator of two C∞symmetries is established. The method is based on a pair of variational C∞-symmetries whose commutators satisfy a certain solvability condition. It allows one to recover a (2n − 2)-parameter family of solutions for the original 2n-th order Euler–Lagrange equation by solving two successive first order ordinary differential equations from the solution of the reduced Euler–Lagrange equation. The procedure is illustrated by two different examples. PACS numbers: 02.30.Xx, 02.30.Hq, 02.20.Sv
منابع مشابه
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