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Quantization and Infinite-Dimensional Systems pp 123–129Cite as

Affine Poisson Structures in Analytical Mechanics

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Abstract

If the space-time is a product of the space and the time the Poisson structure on the phase bundle is used to describe dynamics of mechanical systems. Further it is shown that if the space-time is a fibration over the time, then the Poisson structure has to be replaced by an affine Poisson structure.

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References

  1. S. Benenti, Symplectic relations in analytical mechanics, in: “Modern Developments in Analytical Mechanics”,S. Benenti, M. Francaviglia and A. Lichnerowicz, eds., Atti Accad. Sci. Torino ,Suppl. 117 (1983)

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Author information

Authors and Affiliations

  1. Department of Mathematical Methods in Physics, University of Warsaw, Hoża 74, 00-682, Warszawa, Poland

    Paweł Urbański

Authors
  1. Paweł Urbański
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Editor information

Editors and Affiliations

  1. Catholic University of Louvain, Louvain-la-Neuve, Belgium

    J-P. Antoine

  2. Concordia University, Montréal, Québec, Canada

    S. Twareque Ali

  3. Warsaw University, Białystok, Poland

    W. Lisiecki  & A. Odzijewicz  & 

  4. Bulgarian Academy of Sciences, Sofia, Bulgaria

    I. M. Mladenov

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© 1994 Springer Science+Business Media New York

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Urbański, P. (1994). Affine Poisson Structures in Analytical Mechanics. In: Antoine, JP., Ali, S.T., Lisiecki, W., Mladenov, I.M., Odzijewicz, A. (eds) Quantization and Infinite-Dimensional Systems. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-2564-6_15

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  • DOI: https://doi.org/10.1007/978-1-4615-2564-6_15

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-6095-7

  • Online ISBN: 978-1-4615-2564-6

  • eBook Packages: Springer Book Archive

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