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arXiv · 1112.2523

Functional Lagrange formalism for time-non-local Lagrangians

Luca Ferialdi·Angelo Bassi
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Abstract

We develop a time-non-local (TNL) formalism based on variational calculus, which allows for the analysis of TNL Lagrangians. We derive the generalized Euler-Lagrange equations starting from the Hamilton's principle and, by defining a generalized momentum, we introduce the corresponding Hamiltonian formalism. We apply the formalism to second order TNL Lagrangians and we show that it reproduces standard results in the time-local limit. An example will show how the formalism works, and will provide an interesting insight on the non-standard features of TNL equations.

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Luca Ferialdi, Angelo Bassi. 2011-12-21. Functional Lagrange formalism for time-non-local Lagrangians. https://doi.org/10.1209/0295-5075%2F98%2F30009

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