Remarks on the Nature of Relativistic Particle Orbits

Instantaneous action-at-a-distance relativistic particle dynamics, embraced in Newtonian-like equations of motion χ̈i = Fi(χi, χ̇i) with suitable F's, is examined in once-integrated or ``kinematical'' form χ̇i = fi(χi, Vi) with Vi a set of first integrals transforming as velocities. The Lorentz covariance requirements on fi are worked out and illustrative examples are given, including a family of many-valued ones. A general meaning for integrals of χ̈i = Fi being in involution is adduced, and general counterparts to some well-known theorems in Hamiltonian dynamics are obtained accordingly. A novel elementary proof of the zero-interaction theorem is appended.