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Equations of curves

  1. Mar 9, 2008 #1
    [SOLVED] equations of curves

    a circle of diameter A rolls without slipping along the outer circumference of a stationary circle of the same diameter. use polar coordinates to derive the equation of a curve described by some fixed point on the rolling circle. "can anyone help me out in this?"thanks 4 yo kindness
     
  2. jcsd
  3. Mar 9, 2008 #2

    HallsofIvy

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    Assume the stationary circle has center at (0, 0). Let [itex]\theta[/itex] be the angle the center of the rolling circle makes with the x-axis. Then the center of the rolling circle is distance 2A from the origin and has [itex]x= 2A cos(\theta)[/itex], [itex]y= 2A sin(\theta)[/itex] Now let [itex]\phi[/itex] be the angle the line from the center of the rolling circle to the given point. Then the given point has coordinates [itex]x= A cos(\phi)+ 2A sin(\theta)[/itex] and [itex]y= A sin(\phi)+ 2A sin(\theta)[/itex].

    Of course, [itex]\theta[/itex] and [itex]\phi[/itex] are not independent. Draw a few pictures and right triangles to see how they are related. Then you can replace one by the other to get a single parameter.
     
  4. Mar 13, 2008 #3
    thanks a lot HallsofIvy
     
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