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The Hamilton theories for higher orders classical Lagrange functions resulton a well known Ostrogradski's instabilities. In this work, we propose adifferent definition for the second order canonical momentum and obtain a newset of second order's Hamilton equations. The identity transformationintroduces a new set of constraints depending only on the set of velocities ofall particles and removing the Ostrogradsky's instability. The evolution of thesystem identifies a new set of canonical variables as the poles of theconstraints. The second order momentum shows to be the generator for thenegative displacement of poles of such constraints. The momentum first ordermomentum remains as the generator for the displacement of the coordinate.

Revisiting the Hamilton theory for second order Lagrangian