The Geometry of Higher-Order Lagrange Spaces: Applications to Mechanics and Physics / Edition 1

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This monograph is devoted to the problem of the geometrizing of Lagrangians which depend on higher-order accelerations.
It presents a construction of the geometry of the total space of the bundle of the accelerations of order k>=1. A geometrical study of the notion of the higher-order Lagrange space is conducted, and the old problem of prolongation of Riemannian spaces to k-osculator manifolds is solved. Also, the geometrical ground for variational calculus on the integral of actions involving higher-order Lagrangians is dealt with. Applications to higher-order analytical mechanics and theoretical physics are included as well.
Audience: This volume will be of interest to scientists whose work involves differential geometry, mechanics of particles and systems, calculus of variation and optimal control, optimization, optics, electromagnetic theory, and biology.

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Editorial Reviews

Devoted mostly to the problem of geometrizing Lagrangians that depend on higher-order accelerations. Presents a construction of the geometry of the total space of the bundle of the accelerations when k is equal to or larger than one. Explores the geometry of that space and solves the problem of the prolongation of Riemannian spaces to k-osculator manifolds. Also deals with the geometrical ground for variational calculus on the integral of actions involving higher-order Langrangians and describes applications in higher-order analytical mechanics and theoretical physics. Of interest to scientists working with differential geometry, the mechanics of particles and systems, and related fields. Annotation c. by Book News, Inc., Portland, Or.
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Product Details

  • ISBN-13: 9780792343936
  • Publisher: Springer Netherlands
  • Publication date: 1/31/1997
  • Series: Fundamental Theories of Physics Series, #82
  • Edition description: 1997
  • Edition number: 1
  • Pages: 356
  • Product dimensions: 0.88 (w) x 6.14 (h) x 9.21 (d)

Table of Contents

Preface. 1. Lagrange Spaces of Order 1. 2. The Geometry of 2-Osculator Bundle. 3. N-Linear Connections. 4. Lagrangians of Second Order. Variational Problem. Nöther Type Theorems. 5. Second Order Lagrange Spaces. 6. Geometry of the k-Osculator Bundle. 7. Linear Connections of OsckM. 8. Lagrangians of Order k. Applications to Higher-Order Analytical Mechanics. 9. Prolongation of the Riemannian, Finslerian and Lagrangian Structures to the k-Osculator Bundle. 10. Higher Order Lagrange Spaces. 11. Subspaces in Higher Order Lagrange Spaces. 12. Gauge Theory in the Higher Order Lagrange Spaces. References. Index.

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