  The paper provides mathematics and physics considerations concerning a
special class of electron spin manipulating structures for future Electron-Ion
Collider (EIC) projects. These structures, which we call Universal Synchronous
Spin Rotators (USSR), consist of a sequence of standard basic spin manipulating
elements or cells built with two solenoids and one bending magnet between them.
When integrated into the ring arcs, USSR structures do not affect the central
particle orbit, and their spin transformation functions can be described by a
linear mathematical model. In spite of being relatively simple, the model
allows one to design spin rotators, which are able to perform spin direction
changes from vertical to longitudinal and vice versa in significant continuous
intervals of the electron energy. This makes USSR especially valuable tools for
EIC nuclear physics experiments.
