Noether's theorem on time scales

2007/09/04 by Zbigniew Bartosiewicz, Delfim F. M. Torres · 6 citations
Engineering · Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Nonlinear Differential Equations Analysis #Stability and Controllability of Differential Equations #math-ph #math.CA #math.MP #math.OC #msc:39A12 #msc:49K05

paper · pdf · doi:10.1016/j.jmaa.2008.01.018

published as J. Math. Anal. Appl., Vol. 342, Issue 2, 2008, pp. 1220--1226 · Partially presented at the 6th International ISAAC Congress, August 13 to August 18, 2007, Middle East Technical University, Ankara, Turkey

arxiv created 2007/09/04 · openalex publication_date 2008/01/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We show that for any variational symmetry of the problem of the calculus of variations on time scales there exists a conserved quantity along the respective Euler-Lagrange extremals.

Cited by

• A general backwards calculus of variations via duality
• Variational problems of Herglotz typewith time delay: DuBois--Reymond condition and Noether's first theorem
• Leitmann’s direct method of optimization for absolute extrema of certain problems of the calculus of variations on time scales
• Fractional Calculus on Time Scales
• Calculus of variations on time scales with nabla derivatives
• Delta-nabla optimal control problems

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• Noether's Theorem for Nonsmooth Extremals of Variational Problems with Time Delay