REDUCTION OF SINGULAR LAGRANGIANS OF HIGHER-ORDER
M. de Le\'on, Maria H. Mello and P. R. Rodrigues
Abstract.
Given a singular non-autonomous Lagrangian of higher order we
construct a reduced evolution space of the same order and a
local regular Lagrangian on it which is gauge equivalent to the
original one. The general geometrical framework used is the
theory of almost stable tangent geometry of higher order
introduced in \cite{LORS}. We show that higher order almost
stable manifols can be endowed with a local Poincar\'e-Cartan
form via the inverse problem of Lagrangian Dynamics.
Keywords. Singular, non-autonomous higher order Lagrangians,
connections, inverse problem, reduction, almost stable tangent
geometry.
MS classification: Primary 58F05, 53C15, Secondary 53C05, 70H35, 70H05.
PACS: 0320, 0240.