Abstract
We define a lossless autonomous system as one having a quadratic differential form associated with it, called the total energy, which obeys the property of positivity and which is conserved. In this paper, we show that an autonomous system is lossless if and only if it is oscillatory. Next we discuss a suitable way of splitting the total energy function into its kinetic and potential energy components. We also extend the investigation to the case of open systems.
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