  The Hamilton theories for higher orders classical Lagrange functions result
on a well known Ostrogradski's instabilities. In this work, we propose a
different definition for the second order canonical momentum and obtain a new
set of second order's Hamilton equations. The identity transformation
introduces a new set of constraints depending only on the set of velocities of
all particles and removing the Ostrogradsky's instability. The evolution of the
system identifies a new set of canonical variables as the poles of the
constraints. The second order momentum shows to be the generator for the
negative displacement of poles of such constraints. The momentum first order
momentum remains as the generator for the displacement of the coordinate.

Classical Physics