A recently developed formalism which gives a unified picture of the linear transport of moving frames is extended to include a particular type of transport under the 10-parameter Poincaré group. The frame coordinates are expressed in a 5 × 5 matrix representation which includes the position four-vector plus orthonormal tetrads for the internal coordinates. This provides a general description of the kinematics of physical systems which can be represented by moving frames. Several examples are given, including systems moving with spin (...) and Zitterbewegung along both timelike and null paths. The concept of boost or Poincaré momentum is related to system kinematics. Lagrangians of these systems are also discussed. (shrink)

An outline is given as to how gauge transformations in a frame fiber can be interpreted as defining various types of transport of a moving frame along a path. The cases of general linear, parallel, Lorentz, and other transport groups are examined in Minkowski space-time. A specific set of frame coordinates is introduced. A number of results are obtained including a generalization of Frenet-Serret transport, an extension of Fermi-Walker transport, a relation between frame spaces and certain types of Finsler space, (...) and a derivation of a Kaluza-Klein type metric. Frame transport in general Riemannian space-time is also discussed. (shrink)