ALMOST PRODUCT STRUCTURES IN MECHANICS

Manuel de Le\'on and  David Mart{\'\i}n de Diego

Key words: Presymplectic manifolds, non-holonomic constraints.

1991 Math. Subject Classification: 58F05, 70H33, 70H35.

Abstract: There are two different meanings for constrained systems in
Lagrangian mechanics: ``internal'' constraints imposed by the
singularity of the Lagrangian function, or
``external''cons\-traints imposed by forces of constraint acting
on the  system. In the first case, it is usual to apply the
Gotay-Nester algorithm in the framework of presymplectic
geometry and, in the second case, the classical technique  of
Lagrange multipliers. The aim of this paper it is to give a new
look at singular and non-holonomic Lagrangian systems in the
framework of almost product structures.