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Parametized curves

  1. Oct 5, 2009 #1
    1. The problem statement, all variables and given/known data
    A tank is travelling in a straight line we look at the side on view of the tank and consider its continuous track in contact with the x-axis. Its wheels have radius [tex]R[/tex] and the distance between he centers of the wheels is [tex]L[/tex] (The continuous track is wrapped around the wheels). Consider a point M(t) on the track.

    We suppose that at t = 0 the point M(0) = (0, 0) is on the ground under the centre of
    the back wheel. Give a parametrisation of the curve with respect to the first coordinate
    (denoted by t) of the centre of the back wheel.



    2. Relevant equations



    3. The attempt at a solution
    I'm having diffuculty understanding whether I should get the parametric equation of the curve traced by a fixed point on the track, or the parametric equation of the track in a stationary moving frame
     
    Last edited: Oct 5, 2009
  2. jcsd
  3. Oct 5, 2009 #2

    LCKurtz

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    Draw a side view with the wheels resting on the x axis. Imagine a piece of chalk glued to the wheel at the origin. As the wheels roll to the right the chalk will trace out a curve on your paper. I think that's the curve for which the equations are required.
     
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