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A reduction of order two for infinite-order Lagrangians
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Given a Lagrangian system depending on the position derivatives of any order, and assuming that certain conditions are satisfied, a second-order differential system is obtained such that its solutions also satisfy the Euler equations derived from the original Lagrangian. A generalization of the singular Lagrangian formalism permits a reduction of order keeping the canonical formalism in sight. Finally, the general results obtained in the first part of the paper are applied to Wheeler-Feynman electrodynamics for two charged point particles up to order 1/c4.
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JAÉN, Xavier, LLOSA, Josep and MOLINA, Alfred. A reduction of order two for infinite-order Lagrangians. Physical Review D. 1986. Vol. 34, num. 8, pags. 2302-2311. ISSN 0556-2821. [consulted: 30 of May of 2026]. Available at: https://hdl.handle.net/2445/12322