Dynamic analysis of a two-mass mechanical system in a dissipative medium with allowance for inertial forces

In this paper, a dynamic analysis of a two-mass mechanical system is performed. The aim of this work is to study the effect of the inertial forces of bodies in relative motion within the mechanical system on the motion of this system in a dissipative medium with linear viscous resistance to the motion of one of its bodies (a reference body). The analysis is based on the decomposition of the absolute impulse of the mechanical system into portable and relative components. The resolution shows that the relative inertia forces significantly affect the absolute motion of the mechanical system in a dissipative medium. The equation for such motion is presented, where the total mass of the mechanical system is conditionally concentrated in the reference body. The obtained results and conclusions can be used to solve the problem of two gravitating bodies, one of which is located in a dissipative medium, with the center of mass of the bodies moving relative to the center of the inertial domain. The results are also applicable to three-mass mechanical systems of the inertioid type.