  The jet bundle description of time-dependent mechanics is revisited. The
constraint algorithm for singular Lagrangians is discussed and an exhaustive
description of the constraint functions is given. By means of auxiliary
connections we give a basis of constraint functions in the Lagrangian and
Hamiltonian sides. An additional description of constraints is also given
considering at the same time compatibility, stability and second-order
condition problems. Finally, a classification of the constraints in first and
second class is obtained using a cosymplectic geometry setting. Using the
second class constraints, a Dirac bracket is introduced, extending the
well-known construction by Dirac.
