Recent trends in asymptotical techniques with applications to mechanics

Three important problems of mechanics are addressed. The first corresponds to analytical prediction of a suitable choice of a delay loop parameters in order to control a transitional (perturbed) behaviour of a periodic vibro-impact process modelled by one degree-of-freedom system. The second presents an application of the Melnikov's method to stick-slip chaos prediction in periodically driven self-excited oscillator. The third one illustrates an application of a so called „small 5 method” to analysis of strong non-linear oscillations using example of a mathematical pendulum.