With reference to a rigid symmetrical unbalanced rotor on lubricated journal bearings and adopting the short bearing theory, synchronous orbits and orbits with a 1/2 component described by the journal are determined as approximated solutions of the system of non-linear motion equations. The method also makes it possible to evaluate the stability of the above solutions and thus of the journal orbital motion. For different values of dimensionless unbalance of the rotor, examples of orbits thus obtained are given and, in the modified Sommerfeld number-stability parameter plane, the stability areas of the solutions are identified, in particular, the area of stability of the small synchronous orbits corresponding to the stable operating condition of the rotor-bearings system.

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