On the virial theorem for nonholonomic Lagrangian systems

Cariñena, José F.; Gheorghiu, Irina; Martínez, Eduardo; Santos, Patrícia

doi:10.3934/proc.2015.0204

Cited by 1 publication

(1 citation statement)

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“…Before Georgieva and Guenther, [39] Noether's theorems were applicable only to the classical variational principle and were not applied to the functional defined by different equations. Torres and his co-workers presented Noether's theorem of higher-order variational problems of Herglotz type [40] and Noether's first theorem based on Herglotz variational problems with time delay. [41] Besides, they also proposed Noether's theorem for fractional Herglotz variational problems.…”

Section: Introductionmentioning

confidence: 99%

Noether Symmetry and Conserved Quantities of Fractional Birkhoffian System in Terms of Herglotz Variational Problem

Tian¹,

Zhang²

2018

Commun. Theor. Phys.

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The aim of this paper is to study the Herglotz variational principle of the fractional Birkhoffian system and its Noether symmetry and conserved quantities. First, the fractional Pfaff-Herglotz action and the fractional Pfaff-Herglotz principle are presented. Second, based on different definitions of fractional derivatives, four kinds of fractional Birkhoff's equations in terms of the Herglotz variational principle are established. Further, the definition and criterion of Noether symmetry of the fractional Birkhoffian system in terms of the Herglotz variational problem are given. According to the relationship between the symmetry and the conserved quantities, the Noether's theorems within four different fractional derivatives are derived, which can reduce to the Noether's theorem of the Birkhoffian system in terms of the Herglotz variational principle under the classical conditions. As applications of the Noether's t heorems of the fractional Birkhoffian system in terms of the Herglotz variational principle, an example is given at the end of this paper.

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Section: Introductionmentioning

confidence: 99%