Expressing a circle in the form r(t) = x(t)i + y(t)i +z(t)k

[Lorentz_F]

I learned all the hard (at my level) bits like grad, div, curl and now I'm falling at the first hurdle on the exam papers:

The question is: Express the circle of radius 3, centred at (1,0,3) and lying in the (x,z) plane in the form of r(t) = x(t)i + y(t)j + z(t)k

I was hoping there was someone who wouldn't mind taking me through this step by step especially if there is a simple general equation as I have looked everywhere. And also what to do if it is in the other planes etc.

Thank you,

Laurence

P.s. Sorry if this qualifies as homework, I thought that it didn't.

 

[mathman]

y(t)=0
x(t)=3(cos(t) - 1)
z(t)=3(sin(t) - 3)

When the circle is in a plane perpendicular to one of the axes, it is easy as you can see.

For the general case, it is more complicated. You can set it up in a coordinate system in the given plane and then transform into the global coordinates.

 

[Lorentz_F]

Thanks alot, I don't think i'll be needing anything more complicated than this so greatly appreciated.

Laurence