We review and apply the method of Lagrangian dynamics to particle motion in higher-dimensional spaces. We discuss in detail the case of a Kaluza-Klein theory with coset spaces as fiber. While the total metric we use in general need not allow for Killing vectors, we require that the restriction to the fiber does. We find that for general Jordan-Thiry scalar fields, the geodesic motion in total space is not describable in terms of particle motion in the base manifold with the usual internal charges. The cases when this is possible are discussed. We also consider the geodesic motion in the Sorkin-Gross-Perry Kaluza-Klein monopoles. We find all the conserved quantities and the equations can be integrated by quadrature.