  Assuming the existence of a local vacuum rest frame (LVRF), and using
suitable algebraic tranformations, the internal structure of ultra-high energy
particles (UHEPs) is studied in the presence of Lorentz symmetry violation
(LSV) at the Planck scale. Violations of the standard Lorentz contraction and
time dilation formulae are made explicit. Dynamics in the rest frame of a UHEP
is worked out and discussed. Phenomenological implications for ultra-high
energy cosmic rays (UHECR), including possible violations of the
Greisen-Zatsepin-Kuzmin GZK) cutoff, are studied for several LSV models.
