We consider a second-order variational problem depending
on the covariant acceleration, which is related to 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 Pontryagin’s maximum
principle, allows us to study the dynamics of the control problem.</jats:p
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