Stiffness identification of an impacted constraint is the main issue discussed in this thesis. Primarily, a change of stability (bifurcation) is used to determine the dynamical stiffness of an impacted beam for a piecewise-linear impact oscillator. Detailed one- and two-parameter bifurcation analyses of this impacting system are carried out by means of experiments and numerical methods. Particularly, the two-parameter numerical continuation of the obtained codimension-one bifurcation (period-doubling bifurcation, or fold bifurcation) indicates a strong monotonic correlation between the stiffness of the impacted beam and the frequency at which this bifurcation appears. In addition to the bifurcation techniques, another method for stiffness identification is analysis of impact duration. To accurately detect impact durations from numerical or experimental signals, nonlinear time series methods are utilised. Two impacting systems, including the piecewise-linear impact oscillator and a drillbit-rock vibro-impact system, are studied to demonstrate this proposed method. For either system, the impact duration is relatively constant when the response of oscillator is a period-one one-impact motion, and it is approximated as a half of the natural period of the oscillator-constraint system. When the mass of oscillator is constant, for an impacted constraint with a certain stiffness, the higher the stiffness, the lower the impact duration. This monotonic correlation provides another mechanism to estimate the stiffness of the impacted constraint. Based on the developed two dynamical methods for stiffness identification, a control algorithm for parameter adjustment of the axial vibration for rotary-percussive drilling applications is designed. This control algorithm aims to maintain the optimal drilling state under the varying formations. By this way, the efficiency of rotary-percussive drilling is expected to be promoted.