Non-holonomic equations for the normal extremals in geometric control theory (Q2666641)

The paper under review provides a geometric derivation of the equations for geodesics in sub-Riemannian manifolds. This derivation involves extending the sub-Riemannian metric from the horizontal distribution \(\mathcal{D}\) to the entire tangent bundle, computing the geodesics with respect to a particular connection \(\nabla\), then passing to a limit which blows up lengths in previously chosen complimentary directions \(\mathcal{D}^\perp\). The authors then proceed by providing examples which illustrate this derivation in action. They conclude the paper by explaining how the complementary distribution \(\mathcal{D}^\perp\) can be chosen in some particular settings.