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Zap. Nauchn. Sem. POMI, 2008, Volume 353, Pages 93–115 (Mi znsl1634)  

This article is cited in 8 scientific papers (total in 8 papers)

General properties of planar spiral curves

A. I. Kurnosenko

Moscow Engineering Physics Institute (State University)

Abstract: The paper deals with planar curves with monotone curvature (spirals). Some known facts are generalized by removing requirements of curvature's continuity and constant sign. Necessary and sufficient conditions for the existence of a spiral with given end conditions as well as the existence of the bipolar equation of a spiral are discussed. Bibl. – 8 titles.

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English version:
Journal of Mathematical Sciences (New York), 2009, 161:3, 405–418

Bibliographic databases:

UDC: 514.752.22
Received: 10.01.2007

Citation: A. I. Kurnosenko, “General properties of planar spiral curves”, Geometry and topology. Part 10, Zap. Nauchn. Sem. POMI, 353, POMI, St. Petersburg, 2008, 93–115; J. Math. Sci. (N. Y.), 161:3 (2009), 405–418

Citation in format AMSBIB
\Bibitem{Kur08}
\by A.~I.~Kurnosenko
\paper General properties of planar spiral curves
\inbook Geometry and topology. Part~10
\serial Zap. Nauchn. Sem. POMI
\yr 2008
\vol 353
\pages 93--115
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl1634}
\zmath{https://zbmath.org/?q=an:1182.53003}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2009
\vol 161
\issue 3
\pages 405--418
\crossref{https://doi.org/10.1007/s10958-009-9566-0}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-70350643487}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. I. Kurnosenko, “Korotkie spirali”, Geometriya i topologiya. 11, Zap. nauchn. sem. POMI, 372, POMI, SPb., 2009, 34–43  mathnet; A. I. Kurnosenko, “Short spirals”, J. Math. Sci. (N. Y.), 175:5 (2011), 517–522  crossref
    2. A. I. Kurnosenko, “Dlinnye spirali”, Geometriya i topologiya. 11, Zap. nauchn. sem. POMI, 372, POMI, SPb., 2009, 44–52  mathnet; A. I. Kurnosenko, “Long spirals”, J. Math. Sci. (N. Y.), 175:5 (2011), 523–527  crossref
    3. A. I. Kurnosenko, “O postroenii spirali Kornyu s zadannymi lineinymi elementami na kontsakh”, Geometriya i topologiya. 11, Zap. nauchn. sem. POMI, 372, POMI, SPb., 2009, 53–61  mathnet; A. I. Kurnosenko, “Constructing an arc of Cornu spiral with prescribed linear elements at the endpoints”, J. Math. Sci. (N. Y.), 175:5 (2011), 528–533  crossref
    4. A. I. Kurnosenko, “Postroenie spiralei s zadannymi granichnymi usloviyami”, Geometriya i topologiya. 11, Zap. nauchn. sem. POMI, 372, POMI, SPb., 2009, 62–81  mathnet; A. I. Kurnosenko, “Generating spirals with predefined boundary conditions”, J. Math. Sci. (N. Y.), 175:5 (2011), 534–545  crossref
    5. A. I. Kurnosenko, “Ob odnom svoistve logarifmicheskikh spiralei”, Geometriya i topologiya. 11, Zap. nauchn. sem. POMI, 372, POMI, SPb., 2009, 82–92  mathnet; A. I. Kurnosenko, “On a certain feature of logarithmic spirals”, J. Math. Sci. (N. Y.), 175:5 (2011), 546–553  crossref
    6. Kurnosenko A., “Applying inversion to construct planar, rational spirals that satisfy two-point $G^2$ Hermite data”, Comput. Aided Geom. Design, 27:3 (2010), 262–280  crossref  mathscinet  zmath  isi  elib
    7. Giannelli C., Biard L., “On the interpolation of concentric curvature elements”, Computer-Aided Design, 43:6 (2011), 586–597  crossref  isi  elib
    8. A. I. Kurnosenko, “On the length preserving approximation of plane curves by circular arcs”, Comput. Math. Math. Phys., 57:4 (2017), 590–606  mathnet  crossref  crossref  mathscinet  isi  elib
  • Записки научных семинаров ПОМИ
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