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The Geometry of Higher-Order Hamilton Spaces

Applications to Hamiltonian Mechanics

  • Book
  • © 2003

Overview

Authors:
  1. Radu Miron

    1. Faculty of Mathematics, Al. I. Cuza’ University, Iaşi, Romania

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Part of the book series: Fundamental Theories of Physics (FTPH, volume 132)

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-xvi
    Download chapter PDF

  2. Geometry of the k-Tangent Bundle T k M

    • Radu Miron
    Pages 1-26

  3. Lagrange Spaces of Higher Order

    • Radu Miron
    Pages 27-42

  4. Finsler Spaces of Order k

    • Radu Miron
    Pages 43-57

  5. The Geometry of the Dual of k-Tangent Bundle

    • Radu Miron
    Pages 59-75

  6. The Variational Problem for the Hamiltonians of Order k

    • Radu Miron
    Pages 77-95

  7. Dual Semispray. Nonlinear Connections

    • Radu Miron
    Pages 97-123

  8. Linear Connections on the Manifold T*kM

    • Radu Miron
    Pages 125-149

  9. Hamilton Spaces of Order k ≥ 1

    • Radu Miron
    Pages 151-176

  10. Subspaces in Hamilton Spaces of Order k

    • Radu Miron
    Pages 177-197

  11. The Cartan Spaces of Order k as Dual of Finsler Spaces of Order k

    • Radu Miron
    Pages 199-220

  12. Generalized Hamilton and Cartan Spaces of Order k. Applications to Hamiltonian Relativistic Optics

    • Radu Miron
    Pages 221-234

  13. Back Matter

    Pages 235-247
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Keywords

Reviews

From the reviews:

"The book is devoted to an extensive study of formal-geometric properties of higher-order nondegenerate one-dimensional variational integrals. … The author’s approach is useful for the construction of geometric models … . The book is precisely written, very clear, in principle self-contained and can be understood by non-specialists." (Jan Chrastina, Zentralblatt MATH, Vol. 1044 (19), 2004)

Authors and Affiliations

  • Faculty of Mathematics, Al. I. Cuza’ University, Iaşi, Romania

    Radu Miron

Bibliographic Information

  • Book Title: The Geometry of Higher-Order Hamilton Spaces

  • Book Subtitle: Applications to Hamiltonian Mechanics

  • Authors: Radu Miron

  • Series Title: Fundamental Theories of Physics

  • DOI: https://doi.org/10.1007/978-94-010-0070-3

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media Dordrecht 2003

  • Hardcover ISBN: 978-1-4020-1574-8Published: 31 October 2003

  • Softcover ISBN: 978-94-010-3995-6Published: 18 September 2012

  • eBook ISBN: 978-94-010-0070-3Published: 06 December 2012

  • Series ISSN: 0168-1222

  • Series E-ISSN: 2365-6425

  • Edition Number: 1

  • Number of Pages: XVI, 247

  • Topics: Differential Geometry, Applications of Mathematics

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