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.



Titolo: Functional Lagrange formalism for time-non-local Lagrangians
Autori: 
FERIALDI, LUCA
BASSI, ANGELO
Data di pubblicazione: 2012
Rivista: 
EUROPHYSICS LETTERS  
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.
Handle: http://hdl.handle.net/11368/2629859
Digital Object Identifier (DOI): http://dx.doi.org/10.1209/0295-5075/98/30009
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