Relativistic aspects of the motion of two-particle model molecule oscillating perpendicularly to the direction of its translation

On solving exactly relativistic equations of motion for the model molecule of two particles coupled elastically, it has been shown that in the framework of relativistic mechanics this system, and in general any closed system of interacting particles, is not inertial. In particular, the translational velocity of the mass center of such a system has, as a consequence of the nonlinearity of the equations, oscillatory components reflecting its internal transverse oscillations—it is a pulsed motion. This effect can in principle be seen in the time-of-flight experiments. The force constant of elastic coupling in the system, as seen by the observer at rest, is shown to decline with increase of the total momentum of the system.