The equations of motion are derived for a differentially rotating system, and the paper demonstrates the existence of a force term due to coupling of the angular momentum with the gradient of the angular frequency. Translation of the system of reference to the Local Standard of Rest (LSR) shows that the LSR executes a radial oscillatory motion as a necessary consequence of the coupling mentioned above. This mechanism could well provide the theoretical background for expanding galaxies without resorting to a violent explosion in their centre — a mechanism for which the evidence is rather scanty.