Thank you for your answers. As I understood from equations only ( those fascinating long words in German are amazing but I can understand only a few words :) ), there is a way to solve the spherical pendulum problem without using the elliptic integrals. I think the table from Abramowitz and...
I know that ## \Theta ## in the definition can be whatever I like. As I said I tried various substitutions, even weird ones like ##\frac{cos\Theta}{sin\Theta}=cos\phi ##, or similar to those which where used by Landau in previous problems concerning elliptic integrals. I just can't seem to find...
That's what I thought for a moment. I'm actually using the polish translation of the book, and this expression for effective potential energy is written as a fraction, just as in my first post. In the english version (e.g. this pdf: http://renaissance.ucsd.edu/courses/mae207/mech.pdf) it appears...
Hello everyone. In the 3rd edition of Mechanics by Landau and Lifshitz, paragraph 14, there is a problem concerning spherical pendulum. Calculations leading to the integral $$ t=\int \frac {d \Theta} {\sqrt{\frac{2}{ml^2}[E-U_{ef}(\Theta)]}},$$ $$...