"How to solve parametric systems?"

[WartanThamar]

How can we systematically solve systems of equations that are described by parametric equations, such as those encountered in parametric curve problems or dynamical systems? What are some key techniques for analyzing these systems and finding critical points or steady states? Additionally, what insights or implications can be drawn from solutions to these systems in the context of the broader system behavior?

[janusz55]

Dynamic analysis is the analytical study of the response (i.e. behaviour) of system subjected to a time-varying forcing. Such a study is only possible on the basis of a specific computational model. For real systems, however, proposing an adequate model is only possible if the actual dynamic properties of the modelled object are known. These can only be determined on the basis of appropriate measurements made on that object.
The most common models used in computational practice are those resulting from the application of a discrete description of all (also non-linear) physical properties of the studied objects, e.g. using the finite element method, integration of the equation of motion, frequency and eigenmodes method and modal analysis.