This is a concise review of the symmetries and conserved quantities of the constrained
mechanical systems. It deals with three kinds of symmetries: the Noether symmetry, the Lie …

Two types of nonholonomic systems with symmetry are treated:(i) the configuration space is
a total space of a G-principal bundle and the constraints are given by a connection;(ii) the …

The multisymplectic description of Classical Field Theories is revisited, including its relation
with the presymplectic formalism on the space of Cauchy data. Both descriptions allow us to …

The Hamilton–Jacobi problem is revisited bearing in mind the consequences arising from a
possible bi-Hamiltonian structure. The problem is formulated on the tangent bundle for …

Actions of Lie groups on presymplectic manifolds are analyzed, introducing the suitable
comomentum and momentum maps. The subsequent theory of reduction of presymplectic …

A geometric approach to the method of Lagrange multipliers is presented using the
framework of the tangent bundle geometry. The nonholonomic systems with constraint …

Some aspects of the geometry of jet-bundles, especially relevant for the formulation of
Classical Mechanics, are investigated. The main result is the construction of a tensor …

A geometrical approach to Classical Field Theories: a constraint algorithm for singular theories
Page 1 A geometrical approach to Classical Field Theories: a constraint algorithm for singular …

The aim of this paper is to develop a constraint algorithm for, time-dependent Lagrangian
systems which permit us to solve the motion equations. This algorithm extends the Gotay …

A geometric formulation of Classical Analytical Mechanics, especially suited to the study of
non-holonomic systems is proposed. The argument involves a preliminary study of the …