Thanks for your answer. The problem is that I have two points in spherical coordinates:
$$P_{1}=(\frac{\pi}{4},0)$$
$$P_{2}=(\frac{\pi}{3},\frac{\pi}{2})$$
The great circle which passes through these two points is:
$$\cot(\theta)=\frac{2}{\sqrt{3}}\cdot \sin(\phi+\frac{\pi}{3}-n \cdot...
I'm trying to evaluate the arc length between two points on a 2-sphere.
The geodesic equation of a 2-sphere is:
$$\cot(\theta)=\sqrt{\frac{1-K^2}{K^2}}\cdot \sin(\phi-\phi_{0})$$
According to this article:
http://vixra.org/pdf/1404.0016v1.pdf
the arc length parameterization of the...
Hi everyone!
I'm trying to obtain the natural and dual basis of a circular paraboloid parametrized by:
$$x = \sqrt U cos(V)$$
$$y = \sqrt U sen(V)$$
$$z = U$$
with the inverse relationship:
$$V = \arctan \frac{y}{x}$$
$$U = z$$
The natural basis is:
$$e_U = \frac{\partial \overrightarrow{r}}...
Thank you for your replies! My question now is related to the previous one, but has changed. Suppossing that we have the following situation:
According to the picture, we have a vector in an orthogonal frame (with coordinates 2, 2). I want to obtain the contravariant (green) and covariant...
First of all, thanks for your answer, I really appreciate your quick response.
So, if I have understood well, the first thing I have to do is to represent a vector and relate its components in both coordinate systems using trigonometry:
But, what should I do now? I'm a little confused...
Hi everybody,
This is my first post, so I apologise for all the possible mistakes that I can make now and in the future. I promise that I'll learn from them!
My question is the following: It's well-known the relationship between two pair of cartesian axes when a circular rotation is made...