Numerous systems resist concise characterization through exclusive reliance on either continuous or discrete models, as their dynamics intricately interweave both facets. Neglecting either aspect results in impractical outcomes, providing limited utility for system modeling or controller design. This study revolves around formulating a model for the cyclic walking of the stepladder with a decorator. Comparable to the Compass gait biped walker devoid of ankles and knees, a basic underactuated mechanical system theoretically capable of walking, our focus involves elucidating the mathematical modeling process of this familiar mechanical system featuring hybrid dynamics. Here, the decorator's role is supplanted by an external inertial time-varying force adhering to the d'Alembert principle. Upon identifying the model structure, we engage in a forward parameter study of system dynamics, implemented using a suitable computer algebra system. Subsequently, we undertake the inverse problem of parameter identification, leveraging real data extracted from a video sequence as the subsequent step in our investigation.