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Fractional Birkhoffian mechanics

Luo, Shao-Kai ; Xu, Yan-Li

Acta mechanica, 2015-03, Vol.226 (3), p.829-844 [Periódico revisado por pares]

Vienna: Springer Vienna

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  • Título:
    Fractional Birkhoffian mechanics
  • Autor: Luo, Shao-Kai ; Xu, Yan-Li
  • Assuntos: Biochemistry ; Classical and Continuum Physics ; Construction ; Control ; Derivatives ; Dynamical Systems ; Dynamics ; Engineering ; Engineering Thermodynamics ; Heat and Mass Transfer ; Mathematical analysis ; Mathematical models ; Mechanics ; Oscillators ; Solid Mechanics ; Theoretical and Applied Mechanics ; Transformations ; Vibration
  • É parte de: Acta mechanica, 2015-03, Vol.226 (3), p.829-844
  • Notas: ObjectType-Article-1
    SourceType-Scholarly Journals-1
    ObjectType-Feature-2
    content type line 23
  • Descrição: In this paper, we present a new fractional dynamical theory, i.e., the dynamics of a Birkhoffian system with fractional derivatives (the fractional Birkhoffian mechanics), which gives a general method for constructing a fractional dynamical model of the actual problem. By using the definition of combined fractional derivative, we present a unified fractional Pfaff action and a unified fractional Pfaff–Birkhoff principle, and give four kinds of fractional Pfaff–Birkhoff principles under the different definitions of fractional derivative. And then, by using the fractional Pfaff–Birkhoff principles, we establish a series of fractional Birkhoffian equations with different fractional derivatives and construct the tensor representation of autonomous fractional Birkhoffian equations. Further, we study the relationship among the fractional Bikhoffian system, the fractional Hamiltonian system and the fractional Lagrangian system and give the transformation conditions. And furthermore, as applications of the fractional Birkhoffian method, we construct five kinds of fractional dynamical models, which include the fractional Lotka biochemical oscillator model, the fractional Whittaker model, the fractional Hojman–Urrutia model, the fractional Hénon–Heiles model and the fractional Emden model.
  • Editor: Vienna: Springer Vienna
  • Idioma: Inglês
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  • Realização: ABCD-USP USP   Logos de Redes Sociais: Freepik

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