Metriplectic Euler-Poincaré equations: smooth and discrete dynamics
arxiv(2024)
摘要
In this paper we will study some interesting properties of modifications of
the Euler-Poincaré equations when we add a special type of dissipative force,
so that the equations of motion can be described using the metriplectic
formalism. The metriplectic representation of the dynamics allows us to
describe the conservation of energy, as well as to guarantee entropy
production. Moreover, we describe the use of discrete gradient systems to
numerically simulate the evolution of the continuous metriplectic equations
preserving their main properties: preservation of energy and correct entropy
production rate.
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