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Zapiski Nauchnykh Seminarov POMI, 2009, Volume 372, Pages 62–81 (Mi znsl3558)  
This article is cited in 1 scientific paper (total in 1 paper)

Generating spirals with predefined boundary conditions

A. I. Kurnosenko

Moscow Engineering Physics Institute, Moscow, Russia
Full-text PDF (359 kB) Citations (1)
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Abstract: Spirality, considered as monotonicity of curvature, is preserved under inversions. This property is used to construct a spiral transition curve with predefined curvature elements at the end points. These boundary conditions define two invariant values: Coxeter's inversive distance and the width of the lense. To solve the problem, it is sufficient to realize corresponding values on two curvature elements of any known spiral. The rest is achieved by inversion. In particular, any boundary conditions, compatible with spirality, can be satisfied by inverting an arc of logarithmic spiral. Bibl. – 9 titles.
Key words and phrases: curvature element, transition curve, lenses, bipolar coordinates.
Received: 03.08.2007
English version:
Journal of Mathematical Sciences (New York), 2011, Volume 175, Issue 5, Pages 534–545
DOI: https://doi.org/10.1007/s10958-011-0364-0
Bibliographic databases:
Document Type: Article
UDC: 514.752.22
Language: Russian
Citation: A. I. Kurnosenko, “Generating spirals with predefined boundary conditions”, Geometry and topology. Part 11, Zap. Nauchn. Sem. POMI, 372, POMI, St. Petersburg, 2009, 62–81; J. Math. Sci. (N. Y.), 175:5 (2011), 534–545
Citation in format AMSBIB
\Bibitem{Kur09}
\by A.~I.~Kurnosenko
\paper Generating spirals with predefined boundary conditions
\inbook Geometry and topology. Part~11
\serial Zap. Nauchn. Sem. POMI
\yr 2009
\vol 372
\pages 62--81
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl3558}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2749238}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2011
\vol 175
\issue 5
\pages 534--545
\crossref{https://doi.org/10.1007/s10958-011-0364-0}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79958049730}
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  • https://www.mathnet.ru/eng/znsl/v372/p62
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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