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

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

Mar 1996

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996ap%26ss.244..375p&link_type=abstract

Astrophysics and Space Science, Volume 244, Issue 1-2, pp. 375-385

Astronomy and Astrophysics

Astrophysics

Scientific paper

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.

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