method of Andronow and Witt, Stability for nonlinear problems in mechanics, Perturbations of ordinary differential equations, Nonlinear oscillations and coupled oscillators for ordinary differential equations, classification of singularities, method of van der Pol, stability, Mathieu equation, Phase plane analysis, limit cycles for nonlinear problems in mechanics, Duffing equation, Hill's equation, Vibrations in dynamical problems in solid mechanics, harmonic solutions, Special ordinary differential equations (Mathieu, Hill, Bessel, etc.)