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Nonholonomic constraints

  1. Jan 11, 2012 #1
    So far, every nonholonomic constraint I have seen can be expressed as a collection of inequalities involving the coordinates of the system. For example, a small ball rolling down a sphere with radius a has the constraint [itex]r^2-a^2\geq 0[/itex], where r is the radial coordinate of the ball.

    Can every nonholonomic constraint be written in this form? If not, I would appreciate a counterexample.

    Thanks in advance.
    Last edited: Jan 11, 2012
  2. jcsd
  3. Jan 11, 2012 #2


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    espen180, Nonholonomic means nonintegrable. They can be inequalities, but often they are relationships involving the velocities which can't be integrated to yield a relationship between coordinates. For example when an object rolls without slipping on another, the constraint is an equality between the tangential velocities. Picture a quarter standing up and rolling around on a tabletop.
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