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In this work we consider a second order variational problem depending on the covariant acceleration, which is related with the notion of Riemannian cubic polynomials. This problem and the corresponding optimal control problem are described in the context of higher order tangent bundles using geometric tools. The main tool, a presymplectic variant of the Pontryagin's maximum principle, allows us to study the dynamics of the control problem

Geometric Hamiltonian Formulation of a Variational Problem Depending on the Covariant Acceleration