Geodesic
General properties of planar spiral curves
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 10, Tome 353 (2008), pp. 93-115 
A. I. Kurnosenko. General properties of planar spiral curves. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 10, Tome 353 (2008), pp. 93-115. http://geodesic.mathdoc.fr/item/ZNSL_2008_353_a8/
@article{ZNSL_2008_353_a8,
     author = {A. I. Kurnosenko},
     title = {General properties of planar spiral curves},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {93--115},
     year = {2008},
     volume = {353},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2008_353_a8/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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.

[1] A. I. Kurnosenko, “Interpolyatsionnye svoistva ploskikh spiralnykh krivykh”, Fund. prikl. mat., 7 (2001), 441–463 | MR | Zbl

[2] A. I. Kurnosenko, “Inversnyi invariant pary okruzhnostei”, Zap. nauchn. semin. POMI, 261, 1999, 167–186 | MR | Zbl

[3] H. W. Guggenheimer, Differential Geometry, Dover Publications, New York, 1977 | MR | Zbl

[4] W. Vogt, “Über monotongekrümmte Kurven”, J. Reine Angew. Math., 144 (1914), 239–248 | DOI | Zbl

[5] A. Ostrowski, “Über die Verbindbarkeit von Linien- und Krümmungselementen dürch monoton gekrümmte Kurvebogen”, Enseign. Math. Ser. 2, 2 (1956), 277–292 | MR | Zbl

[6] K. M. Bolton, “Biarc curves”, Computer-Aided Design, 7:2 (1975), 89–92 | DOI

[7] S. B. Jackson, “Vertices of plane curves”, Bull. Amer. Math. Soc., 50 (1944), 564–578 | DOI | MR | Zbl

[8] B. M. Cherdak, “Ogranichennost krivykh, zadannykh svoimi kriviznami”, Uchën. zap. Leningrad. ped. in-ta im. A. I. Gertsena, 274 (1965), 202–212 | Zbl