Reynolds transport theorem for smooth deformations of currents on manifolds

Lior Falach, Reuven Segev

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

The Reynolds transport theorem for the rate of change of an integral over an evolving domain is generalized. For a manifold B, a differentiable motion m of B in the manifold S, an r-current T in B, and the sequence of images m(t)#T of the current under the motion, we consider the rate of change of the action of the images on a smooth r-form in S. The essence of the resulting computations is that the derivative operator is represented by the dual of the Lie derivative operation on smooth forms.

Original languageEnglish
Pages (from-to)770-786
Number of pages17
JournalMathematics and Mechanics of Solids
Volume20
Issue number6
DOIs
StatePublished - 3 Jul 2015

Keywords

  • Lie derivative
  • Reynolds transport theorem
  • de Rham currents
  • differentiable manifolds
  • homotopy formula

ASJC Scopus subject areas

  • General Mathematics
  • General Materials Science
  • Mechanics of Materials

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