Solve Equations of Curves - Get Help Now!

[wilhelmsir]

[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

 

[HallsofIvy]

Assume the stationary circle has center at (0, 0). Let \theta 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 x= 2A cos(\theta), y= 2A sin(\theta) Now let \phi be the angle the line from the center of the rolling circle to the given point. Then the given point has coordinates x= A cos(\phi)+ 2A sin(\theta) and y= A sin(\phi)+ 2A sin(\theta).

Of course, \theta and \phi 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.

 

[wilhelmsir]

thanks a lot HallsofIvy