Relativistic length contraction and time dilation as dynamical phenomena

It is commonly accepted that a rod after having been accelerated and then left free contracts by the Lorentz factor, and also that the clock after having been accelerated and then returned to rest exhibits time dilation in accordance with the proper time formula. Although both issues have been debated numerous times, no models have been proposed to trace the dynamical nature of these phenomena. The purpose of the present paper is to propose a simple relativistic model of an elastic rod, which allows exact analytical solutions for a number of problems. The solutions of two problems are presented: 1) acceleration of the rod by a constant force applied at one of its ends during a finite time interval, resulting in the Lorentz contraction, 2) acceleration and deceleration of a light clock, resulting in time dilation.