On the relation between energy-conserving low-order models and a system of coupled generalized volterra gyrostats with nonlinear feedback

摘要

In this paper we first prove the equivalence between the system of coupled Volterra gyrostats and a special class of energy-conserving low-order models. We then extend the definition of the classical Volterra gyrostat to include nonlinear feedback, resulting in a class of generalized Volterra gyrostats. Using this new class of gyrostats as a basic building block, we present an algorithm for converting a general class of energy-conserving low-order models that routinely arise in fluid dynamics, turbulence, and atmospheric sciences into a system of coupled generalized Volterra gyrostats with nonlinear feedback.