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A formulation of singular classical theories (determined by degenerateLagrangians) without constraints is presented. A partial Hamiltonian formalismin the phase space having an initially arbitrary number of momenta (which canbe smaller than the number of velocities) is proposed. The equations of motionbecome first-order differential equations, and they coincide with those ofmulti-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 ofgeneralized momenta with the rank of the Hessian matrix. The noncanonicalgeneralized velocities satisfy a system of linear algebraic equations, whichallows 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 ourformulation) extension of the phase space. In this case the new brackettransforms into the Dirac bracket. Quantization is briefly discussed.

Formulation of singular theories in a partial Hamiltonian formalism using a new bracket and multi-time dynamics