  A formulation of singular classical theories (determined by degenerate
Lagrangians) without constraints is presented. A partial Hamiltonian formalism
in the phase space having an initially arbitrary number of momenta (which can
be smaller than the number of velocities) is proposed. The equations of motion
become first-order differential equations, and they coincide with those of
multi-time dynamics, if a certain condition is imposed. In a singular theory,
this condition is fulfilled in the case of the coincidence of the number of
generalized momenta with the rank of the Hessian matrix. The noncanonical
generalized velocities satisfy a system of linear algebraic equations, which
allows an appropriate classification of singular theories (gauge and nongauge).
A new antisymmetric bracket (similar to the Poisson bracket) is introduced,
which describes the time evolution of physical quantities in a singular theory.
The origin of constraints is shown to be a consequence of the (unneeded in our
formulation) extension of the phase space. In this case the new bracket
transforms into the Dirac bracket. Quantization is briefly discussed.
