Reverse motions of mechanical systems

The possibility of the occurrence of sections of reverse motions in natural mechanical systems, when, in the second half of a time interval, the motion in the first half of the interval is repeated in the reverse order and the opposite velocity with a specified accuracy, is investigated. It is shown that such motions are characteristic of natural mechanical systems in the neighbourhood of a non-degenerate equilibrium position if the natural frequencies are independent. Systems with gyroscopic and dissipative forces are also considered. It is shown that, in these systems, sections of reverse motion can be observed in a special system of coordinates. Examples are presented.