Abstract
In this article, an engineering/physical dynamic system including losses is analyzed inrelation to the stability from an engineer’s/physicist’s point of view. Firstly, conditions for a
Hamiltonian to be an energy function, time independent or not, is explained herein. To analyze
stability of engineering system, Lyapunov-like energy function, called residual energy function
is used. The residual function may contain, apart from external energies, negative losses as
well. This function includes the sum of potential and kinetic energies, which are special forms
and ready-made (weak) Lyapunov functions, and loss of energies (positive and/or negative)
of a system described in different forms using tensorial variables. As the Lypunov function,
residual energy function is defined as Hamiltonian energy function plus loss of energies and
then associated weak and strong stability are proved through the first time-derivative of residual
energy function. It is demonstrated how the stability analysis can be performed using the residual
energy functions in different formulations and in generalized motion space when available.
This novel approach is applied to RLC circuit, AC equivalent circuit of Gunn diode oscillator
for autonomous, and a coupled (electromechanical) example for nonautonomous case. In
the nonautonomous case, the stability criteria can not be proven for one type of formulation,
however, it can be proven in the other type formulation.
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