  The relativistic jerk, snap and all higher-order kinematical D-vectors are
defined for the motion of a massive particle in a D-dimensional Minkowski
spacetime. We illustrate the formalism with stationary motions, for which we
provide a new, Lorentz covariant, classification. We generalize some cases to
branes, explaining the relevance to uniform motion in a heat bath. We also
consider some non-stationary motions, including motion with constant proper
jerk, and free fall into a black hole as viewed from a GEMS perspective.
