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Astrophysics and Space Science

, Volume 244, Issue 1–2, pp 375–385 | Cite as

Some elementary geometric aspects in extending the dimension of the space of instants

  • A. P. Pitucco
Session 7. Mathematical Models and Methods
  • 22 Downloads

Abstract

A local geometric construction is proposed on thepartially ordered set of instantsI. A totally ordered subsetC(I)I is assumed to have 3-dimensional affine coordinate structure,without a specified metric, called the τ-space ofC(I). Guided by a strong analogy with analytical mechanics theT-configuration space (θ, τα), θ a real parameter, is constructed where-upon the usual Hamilton-Jacobi theory establishes a simple geometrical construction, viz., the complete figure from the calculus of variations. The duration function, dur:C(I)R is associated withtemporally equidistant hypersurfaces through which pass a congruence of extremal curves to the fundamental integral.

Keywords

Analytical Mechanic Real Parameter Geometric Construction Geometric Aspect Coordinate Structure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • A. P. Pitucco
    • 1
  1. 1.Department of PhysicsPima County Community College West CampusTucson

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