We demonstrate how to construct many different Lagrangians for two famous examples that were deemed by Douglas (1941 Trans. Am. Math. Soc. 50 71-128) not to have a Lagrangian. Following Bateman's dictum (1931 Phys. Rev. 38 815-9), we determine different sets of equations that are compatible with those of Douglas and derivable from a variational principle.
M.C. Nucci, P.G.L. Leach (2011). Some Lagrangians for Systems without a Lagrangian. PHYSICA SCRIPTA, 83(3), 035007-1-035007-5 [10.1088/0031-8949/83/03/035007].
Some Lagrangians for Systems without a Lagrangian
M.C. Nucci;
2011
Abstract
We demonstrate how to construct many different Lagrangians for two famous examples that were deemed by Douglas (1941 Trans. Am. Math. Soc. 50 71-128) not to have a Lagrangian. Following Bateman's dictum (1931 Phys. Rev. 38 815-9), we determine different sets of equations that are compatible with those of Douglas and derivable from a variational principle.File in questo prodotto:
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