report · ResearchSpace (University of Auckland) · 1999

Brachistochrones for Repulsive Inverse Square Force

Cited by 1Abstract and details only

Abstract

Brachistochrones for inverse square repulsion are expressed in terms of elliptic integrals, as for inverse square attraction. But, the set of brachistochrones is much more complicated than for inverse square attraction. Each pair of points is connected by infinitely many brachistochrones, on each of which the passage time is a local minimum, and the global minimum passage time is attained on one (or on infinitely many) of those curves. The bounded brachistochrones starting at a fixed point are separated from the unbounded brachistochrones by a Critical Brachistochrone, which is expressed in terms of elementary functions.

Cite this paper

APA 7

Tee, G. J. (1999). Brachistochrones for Repulsive Inverse Square Force. ResearchSpace (University of Auckland).

MLA 9

Tee, Garry J. “Brachistochrones for Repulsive Inverse Square Force.” ResearchSpace (University of Auckland), 1999.

Chicago

Tee, Garry J. 1999. “Brachistochrones for Repulsive Inverse Square Force.” ResearchSpace (University of Auckland).

Harvard

Tee, G.J. (1999) ‘Brachistochrones for Repulsive Inverse Square Force’, ResearchSpace (University of Auckland).

BibTeX

@article{tee1999brachistochrones,
  title = {{Brachistochrones for Repulsive Inverse Square Force}},
  author = {Tee, Garry J.},
  journal = {ResearchSpace (University of Auckland)},
  year = {1999}
}

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