Abstract
The formalism of classical mechanics is extended to yield an energy function analysis of single degree of freedom, linear time-varying networks. With the aid of the newly found modifications of the classical Lagrangian and Hamiltonian, the behavior of the single loop R(t) - L(t) - C(t) network is discussed through analogy with familiar classical quantities. The Hamiltonian formulation, through its associated canonical equations, leads to a qualitative phase plane specification of single degree of freedom network behavior. Moreover, the Hamiltonian formulation leads directly to stability criteria which are expressed in terms of the network element values only. Upper and lower bounding functions for the network stored energy are obtained which lead to separate necessary and sufficient conditions for network stability.
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