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The intrinsic linearization of equilibria of nonholonomic systems

Letters in Mathematical Physics volume 108, pages 2487–2490 (2018)Cite this article

Abstract

The linearization of equilibria of Hamiltonian systems is Hamiltonian; this has well-known and important implications for the spectrum. The analogous statement for nonholonomic systems is provided. It follows, for example, that the linearization of the ground state of a nonholonomic system is always Hamiltonian.

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References

  1. Abraham, R., Marsden, J.E.: Foundations of Mechanics, 2nd edn. Addison-Wesley, Boston (1978)

    MATH  Google Scholar 

  2. Bates, L., Sniatycki, J.: Nonholonomic reduction. Rep. Math. Phys. 32, 99–115 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  3. Meyer, K.R., Hall, G.R.: Introduction to Hamiltonian Dynamical Systems and the \(N\)-Body Problem. Springer, New York (1991)

    MATH  Google Scholar 

  4. Patrick, G.W.: Variational development of the geometry of nonholonomic mechanics. Rep. Math. Phys. 59, 145–184 (2007)

    Article  ADS  MathSciNet  Google Scholar 

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  1. Department of Mathematics and Statistics, University of Saskatchewan, Saskatoon, S7N 5E6, Canada

    George W. Patrick

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  1. George W. Patrick
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Correspondence to George W. Patrick.

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Patrick, G.W. The intrinsic linearization of equilibria of nonholonomic systems. Lett Math Phys 108, 2487–2490 (2018). https://doi.org/10.1007/s11005-018-1089-5

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  • DOI: https://doi.org/10.1007/s11005-018-1089-5

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