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Math Help - Reparametrization of tractrix

  1. #1
    Junior Member HAL9000's Avatar
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    Reparametrization of tractrix

    Hello!

    I wonder how to choose a reparametrization map, so that I can transfrom the curve given by

    c_1(t)=(\sin t, \cos t + \ln \tan (t/2))

    to

    c_2(t)=(\frac{1}{\cosh t},t-\tanh t)

    ...and vice versa.

    Can't see it at the moment.
    Any ideas?

    Thanks in advance
    Last edited by HAL9000; November 7th 2011 at 08:31 AM.
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: Reparametrization of tractrix

    For example, if t=\arcsin \left(\frac{1}{\cosh u}\right) , then \cos t=\ldots=\pm \tanh u etc .
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