Acta Applicandae Mathematicae

, Volume 162, Issue 1, pp 121–143 | Cite as

Hamiltonian Symmetry Reduction via Localizations: Theory and Application to a Barbell System

  • Jürgen ScheurleEmail author
  • Sebastian Walcher


We specialize a recently introduced variant of orbit space reduction for symmetric Hamiltonian systems. This variant works with suitable localizations of the algebra of polynomial invariants of the corresponding symmetry group action, and provides reduction to a variety that is embedded in a low-dimensional affine space, which makes efficient computations possible. As an example, we discuss the mechanical system of a “barbell” in a general central force field.


Linear groups Invariant theory Hamiltonian systems with symmetry Relative equilibria 

Mathematics Subject Classification

34C20 13A50 34C14 37C80 



The authors thank anonymous reviewers of the present and an earlier version of this paper for helpful comments, and they gratefully acknowledge the support of the Research in Pairs (RIP) program of Mathematisches Forschungsinstitut Oberwolfach (MFO) in 2017.


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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Zentrum MathematikTU MünchenGarchingGermany
  2. 2.Lehrstuhl A für MathematikRWTH AachenAachenGermany

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