Energy storage elements are dynamic elements

Why do we need to know about dependent energy storage elements?

This is a typical consequence of dependent energy storage elements and, as one might expect, in more complex systems the algebraic manipulations can become formidable, even prohibitively so. It would be useful to know about dependent energy-storage elements before attempting to derive equations. How may we do so?

Is energy storage a static or memory-less function?

Note that although we will use energy storage elements to describe dynamic behavior, this constitutive equation is a static or memory-less function. The constitutive equation permits us to evaluate the generalized potential energy, Ep For this element, potential energy is a function of displacement alone.

What is inter-dependence of energy storage elements?

That is the true meaning of inter-dependence of energy storage elements: in the model they are not distinct energy storage elements, despite appearances to the contrary. These two modelling approximations — rigid-body models and time-derivative operations — are intimately related.

Why are energy storage elements not independent?

Because the two energy storage elements in this model are not independent. Because of the one-junction, the velocity or momentum of one determines the velocity or momentum of the other; given the masses of both bodies, knowing the energy of one is sufficient to determine the energy of the other.

What are the two energy storage mechanical elements?

The two energy storage mechanical elements can have initial conditions that need to be taken into account in the analysis. A mass can have an initial velocity, which will clearly produce a force, and a spring can have a nonzero rest length, which also produces a force.

Does every energy storage element have a state variable?

In the foregoing examples we found that one state variable was associated with the energy stored in each energy storage element. Will every energy storage element give rise to an unique state variable? Not necessarily, as we will see below when we consider two energy storage elements of the same type connected by a simple junction.