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The brachistochrone with acceleration: A running track

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Abstract

The equations for the brachistochrone of a self-accelerating particle are found by solving a problem in the calculus of variations with a constraint and a free end condition then applied to find the shape of a running track.

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References

  1. Bolza, O.,Über den Anormalen Fall beim Lagrangeschen und Mayerschen Problem mit Gemischten Bedingungen und Variabeln Endpunkten, Mathematische Annalen, Vol. 74. 1913.

  2. Bliss, G. A.,The Problem of Bolza in the Calculus of Variations, Annals of Mathematics, Vol. 33, 1932.

  3. Bliss, G. A.,Lectures on the Calculus of Variations, The University of Chicago Press, Chicago, 1946.

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Authors and Affiliations

  1. Department of Applied Mathematics, School of General Studies, Australian National University, Canberra, Australia

    J. E. Drummond (Reader) & G. L. Downes (Research Assistant)

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  1. J. E. Drummond
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  2. G. L. Downes
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Communicated by D. Lawden

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Drummond, J.E., Downes, G.L. The brachistochrone with acceleration: A running track. J Optim Theory Appl 7, 444–449 (1971). https://doi.org/10.1007/BF00931980

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  • DOI: https://doi.org/10.1007/BF00931980

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