Polar-parametric transformation

1. Dec 17, 2004

Moore1879

Is it possible to transform a parametric "equation" into a polar equation? If so how would I go about it?

2. Dec 17, 2004

dextercioby

If the fomulae relating various coordinate systems are diffemorphisms,then why not??Bring an example.A (plane) curve in parametric coordinates.And tell us what u gave to do to express it in (plane) polar coordinates.

Daniel.

3. Dec 17, 2004

Moore1879

If I'm given the parametric equations for a hypocycloid:
x(t)=(a/n)[(n-1)cos(t)-cos[(n-1)t]
y(t)-(a/n)[(n-1)sin(t)+sin[(n-1)t]

how would I go about putting it into a function form $$r(\theta)[\tex]. There has to be some way to do it. What would it be? Thanks 4. Dec 17, 2004 Moore1879 If I'm given the parametric equations for a hypocycloid: x(t)=(a/n)[(n-1)cos(t)-cos[(n-1)t] y(t)-(a/n)[(n-1)sin(t)+sin[(n-1)t] how would I go about putting it into a function form [tex]r(\theta)$$.
There has to be some way to do it. What would it be?

Thanks

5. Dec 17, 2004

dextercioby

That's a horrible curve... :yuck: Anyway'ill let u do the calculations of eliminating the parameter.
$$\rho (t)=\sqrt{x^{2}(t)+y^{2}(t)}$$
$$\theta(t)=\arctan({\frac{y(t)}{x(t)}})$$

Express $t(\theta)$ and plug it into $\rho(t)$.

Daniel.

PS.My advice:GIVE UP!!It's enough to know that it's possible.

Last edited: Dec 17, 2004
6. Dec 17, 2004

Moore1879

Thanks Kurt? I assume that is your name. That is all I needed. Oh, and I'm not going to give it up.

7. Dec 17, 2004

dextercioby

:rofl: :rofl: :rofl: :rofl: :rofl: My name is Daniel.I write it all the time.
That is a "signature".It's edited from the "USER CP" box.Kurt Lewin was a theorist and i loved his idea and decided to quote him.

Daniel.Really,no bull****.

8. Dec 18, 2004

arildno

It's much easier to find $$t(\rho)$$ than $$t(\theta)$$
Then, you might invert $$\theta(\rho)$$ into $$\rho(\theta)$$
the inversion is practically impossible to perform, so I concur with Daniel's advice.