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A Formulation of Hamiltonian Mechanics Using Geometric Calculus

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Clifford Algebras and their Applications in Mathematical Physics

Part of the book series: Fundamental Theories of Physics ((FTPH,volume 55))

Abstract

The Clifford-algebra-based geometric calculus developed by Hestenes and Sobczyk is used to formulate some of the key concepts and theorems of Hamiltonian mechanics A brief comparison with other formulations is made.

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References

  1. E.T. Whittaker (1937), A Treatise on the Analytical Dynamics of Particles and Rigid Bodies, Cambridge Univ. Press, London/New York.

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  2. H.C. Corben and P. Stehle (1960), Classical Mechanics, John Wiley & Sons, Inc., New York.

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  3. V.I. Arnold (1978), Mathematical Methods of Classical Mechanics, Springer-Verlag, New York.

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  4. D. Hestenes (1993), “Hamiltonian Mechanics with Geometric Calculus”, in Spinors, Twistors and Clifford Algebras, Z. Isiewicz, A. Borowics, and B. Jancewicz (eds) [To be published by Kluwer Acad. Publishers.]

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  5. D. Hestenes and G. Sobczyk (1984), Clifford Algebra to Geometric Calculus, D. Reidel Publishing Co., Dordrecht/Boston.

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  6. A Lichnerowicz (1977), “Les variétés de Poisson et leurs algèbres de Lie associées”, J. Differential Geometry 12, 253–300.

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  7. D. Hestenes (1986), New Foundations for Classical Mechanics, D. Reidel Publishing Co., Dordrecht/Boston.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Widener University, Chester, PA, 19013, USA

    Richard C. Pappas

Authors
  1. Richard C. Pappas
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Editor information

Editors and Affiliations

  1. Department of Mathematical Analysis, University of Ghent, Ghent, Belgium

    F. Brackx , R. Delanghe  & H. Serras ,  & 

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© 1993 Kluwer Academic Publishers

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Pappas, R.C. (1993). A Formulation of Hamiltonian Mechanics Using Geometric Calculus. In: Brackx, F., Delanghe, R., Serras, H. (eds) Clifford Algebras and their Applications in Mathematical Physics. Fundamental Theories of Physics, vol 55. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2006-7_29

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  • DOI: https://doi.org/10.1007/978-94-011-2006-7_29

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-0-7923-2347-1

  • Online ISBN: 978-94-011-2006-7

  • eBook Packages: Springer Book Archive

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