Noether’s Theorems and the Direct Method

  • Gary Webb
Part of the Lecture Notes in Physics book series (LNP, volume 946)


In this chapter we give a general discussion of Noether’s theorems and the Calculus of Variations, for systems of differential equations governed by a variational principle. Noether’s theorems are discussed by Gelfand and Fomin (1963), Ibragimov (1985), Marsden and Ratiu (1994), Holm (2008a,b), Bluman and Kumei (1989)), Olver (1993), Anco and Bluman (1996, 1997, 2002a,b), and Bluman et al. (2010) and others. We use the analysis of Bluman and Kumei (1989) and Ibragimov (1985) as summarized by Webb et al. (2005b). Hydon and Mansfield (2011) give a clear presentation of Noether’s second theorem. The main aim is to briefly present Noether’s theorems and methods to derive conservation laws. Noether’s theorems link the symmetries of the action and conservation laws, for systems of differential equations governed by a variational principle.


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© Springer International Publishing AG 2018

Authors and Affiliations

  • Gary Webb
    • 1
  1. 1.CSPARThe University of Alabama in HuntsvilleHuntsvilleUSA

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