conversion to polar coordinates
Nov. 19th, 2005 03:19 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
paperclippySo I have x and y velocities, and I want speed and angular velocity. Is the following correct?
r = sqrt(x^2 + y^2)
theta = invtan(y/x)
so
dr/dt = (1/2) * (1/sqrt(x^2+y^2)) * (2x(dx/dt) + 2y(dy/dt))
dtheta/dt = (1/(1 + (y/x)^2))*((x(dy/dt) - y(dx/dt))/x^2)
Assuming I took derivatives correctly. The question is: is there a way to get dr/dt and dtheta/dt without knowing x and y? What if I only know dx/dt and dy/dt?
r = sqrt(x^2 + y^2)
theta = invtan(y/x)
so
dr/dt = (1/2) * (1/sqrt(x^2+y^2)) * (2x(dx/dt) + 2y(dy/dt))
dtheta/dt = (1/(1 + (y/x)^2))*((x(dy/dt) - y(dx/dt))/x^2)
Assuming I took derivatives correctly. The question is: is there a way to get dr/dt and dtheta/dt without knowing x and y? What if I only know dx/dt and dy/dt?
