A partially explicit construction of a Lagrange-Hamiltonian formalism for an arbitrary n -dimensional Newtonian system of equations of motion is given. Additional variables used in the construction are spontaneously reduced by the Dirac’s constraints resulting from degeneracy of the proposed Lagrangian, so that only the variables that appear in the original system of equations remain. A Hamiltonian and dynamical Dirac’s brackets are calculated.
Hebda, Piotr W. and Hebda, Beata A., "Spontaneous Dimension Reduction and the Existence of a local Lagrange-Hamilton Formalism for Given n-Dimensional Newtonian Equations of Motion" (2015). Faculty Publications. 2.