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Seeking a example of noholonomic constraint

  1. Apr 19, 2015 #1
    I was reading up classical mechanics in Goldstein but needed some clarifications. I looked online and saw something that bothers me qutie a bit. In the online pdf below, on page 69 (or 74th screen scrolls), it states that Dot Cancellation does not work if the position vector is a function of BOTH generalized coordinates AND generalized velocities such that \vec_r = \vec_r(q_1, q_2, ...; \dot_q_1, \dot_q_2, \dot_q_3). On top, the PDF states that it happens for certain non-holonomic constraints. Since this dot cancellation is central to using D'Alembert's principle to arrive at the form of Euler-Lagrange Equations. I am wondering where this Dot Cancellation would fail.

    Dot Cancellation: d(\vec_r)/dq = d(\vec_v)/d(\dot_q)
    http://www.astro.caltech.edu/~golwala/ph106ab/ph106ab_notes.pdf

    Question:
    Would someone kindly give me an example such that the position vector \vec_r actually depends on generalized velocities as well as the constraints that causes it please? Thanks much.
     
    Last edited: Apr 19, 2015
  2. jcsd
  3. Apr 24, 2015 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
     
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