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In this paper the dynamics of a non-linear system with non-ideal excitation are studied. An unbalanced motor with a strong non-linear structure is considered. The excitation is of non-ideal type. The model is described with a system of two coupled strong non-linear differential equations. The steady state motions and their stability is studied applying the asymptotic methods. The existence of the Sommerfeld effect in such non-linear non-idealy excited system is proved. For certain values of system parameters chaotic motion appears. The chaos is realized through period doubling bifurcation. The results of numerical simulation are plotted and the Lyapunov exponents are calculated. The Pyragas method for control of chaotic motion is applied. The parameter values for transforming the chaos into periodical motion are obtained.

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In this paper a non-ideal mechanical system with clearance is considered. The mechanical model of the system is an oscillator connected with an unbalanced motor. Due to the existence of clearance the connecting force between motor and the fixed part of the system is discontinuous but linear. The mathematical model of the system is represented by two coupled second-order differential equations. The transient and steady-state motion and also the stability of the system are analyzed. The Sommerfeld effect is detected. For certain values of the system parameters the motion is chaotic. This is caused by the period doubling bifurcation. The existence of chaos is proved with maximal Lyapunov exponent. A new chaos control method based on the known energy analysis is introduced and the chaotic motion is transformed into a periodic one.