- #1
davidbenari
- 466
- 18
I'm reading the professors notes and he gives this general equation for the ellipse. The professor has already been mistaken in some of his notes so I wanted you to help me validate what he's saying, as I can't prove the equation.
Suppose we have the vector ##\mathbf{r}=\big(x_o \cos(-\omega t + \phi_x), y_o \cos(-\omega t +\phi_y)\big)##
Then, he says that the general equation for the path is:
##\frac{x}{x_o}^2+\frac{y}{y_o}^2-\frac{2xy}{x_oy_o}\cos\delta=\sin^2\delta##
where ##\delta=\phi_y-\phi_x##.
So my question was where does this equation come from? How can I derive it? I know these type of equations are tedious to prove so it's okay if you give me a rough outline, or point me towards a source which does go through it. Or at least tell me you attest to its validity. I can't find the equation elsewhere and I haven't been able to prove it myself.
Thanks.
Suppose we have the vector ##\mathbf{r}=\big(x_o \cos(-\omega t + \phi_x), y_o \cos(-\omega t +\phi_y)\big)##
Then, he says that the general equation for the path is:
##\frac{x}{x_o}^2+\frac{y}{y_o}^2-\frac{2xy}{x_oy_o}\cos\delta=\sin^2\delta##
where ##\delta=\phi_y-\phi_x##.
So my question was where does this equation come from? How can I derive it? I know these type of equations are tedious to prove so it's okay if you give me a rough outline, or point me towards a source which does go through it. Or at least tell me you attest to its validity. I can't find the equation elsewhere and I haven't been able to prove it myself.
Thanks.