We study simple splines on a Riemannian manifold Q from the point of view of the Pontryagin maximum principle (PMP) in optimal control theory. The control problem consists in finding smooth curves matching two given tangent vectors with the control being the curve’s acceleration, while minimizing a given cost functional. We present a general strategy to solve for the optimal hamiltonian
within the PMP framework based on splitting the variables by means of a
linear connection. We will discuss possible appĺications and generalizations.