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Zum Integrationsproblem sphärischer Hüllkurvenpaare

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Abstract

Since H.R. MüLLER [1] it is well known that spherical envelope pairs X,X′ to a given roll sliding number are solutions of two conjugate Riccati differential equations. For two special cases an integral is known [1,3]. By use of the fundamental differential equations of the polodes [2] we show the existence of two classes of integrable curves X,X′.

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Literatur

  1. H.R. MÜLLER, Zur Kinematik des Rollgleitens II (Sphärisches Rollgleiten), Arch.Math. VI (1955) 471–480.

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  2. J. TÖLKE, Spezielle Bewegungsvorgänge III, Arch.Math. XXI (1970) 650–659.

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  3. J. TÖLKE, Oskulierende sphärische Hüllkurvenpaare, Sb.Österr.Ak.Wiss.(math.-nat.)Kl II181 (1973) 71–75.

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Authors and Affiliations

  1. Fachbereich Mathematik, Gesamthochschule Siegen, Hölderlinstraße 3, 5900, Siegen 21

    Jürgen Tölke

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  1. Jürgen Tölke
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Herrn Professor Dr. H.R. Müller zum 65. Geburtstag gewidmet

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Tölke, J. Zum Integrationsproblem sphärischer Hüllkurvenpaare. Manuscripta Math 19, 189–194 (1976). https://doi.org/10.1007/BF01275421

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  • DOI: https://doi.org/10.1007/BF01275421

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