The approximate calculation of limit cycles of a single wheelset on straight and curved track was demonstrated in /2, 4/:

The spatial kinematics of the wheel rail system with arbitrary profiles are analysed by solving a system of nonlinear algebraic equations. Nonlinear expressions for the creepages on straight and curved track are derived. The spatial kinetics of the wheel rail system on straight and curved track are expanded using Newton-Euler or Lagrangian methods. The nonlinear differential equations of motion are transformed by means of a fourier series expansion into quasilinear differential equations and then into nonlinear algebraic equations. Frequency, amplitudes and phases of possible limit cycles are solutions of these equations.

In this paper the limit cycles of a bogie with either rigid, elastic or creep-controlled wheelsets on straight and curved track are presented. In addition to these passive and semiactive systems two types of active wheelsets are analysed by applying yaw moments and by applying periodic traction moments.

The analysis concentrates on the evaluation of the rotational velocity of the wheel discs resp. wheelsets. These rotational degrees of freedom are important, if a powered bogie is designed as an integrated traction unit, where wheelsets, bogie and traction motors are treated as a complex electromechanical unit.