How to Integrate Kepler's Problem in Landau Mechanics?

[physicophysiology]

Hello
I am studying Landau Mechanics (3rd ed.)

In chapter III Integration of the Equations of Motions
§15. Kepler's problem
page 36

M(angular momentum), m(mass), E(mechanical energy), and α are constant.

How to integrate it?
Please help me...

 

[jedishrfu]

If you’re just trying to verify that’s it’s true then differentiate the integrated side to prove to yourself.

To integrate it though, I would use integral tables and look up a similar one. There is no shame in using this approach as there are many integrals that vex even the best folks.

A cheap book with integral tables is Schaums outlines on Math Tables and Formulas. It’s available on Amazon and is a great reference to keep around.

 

[berkeman]

I SOLVED IT
HOW CAN I DELETE THIS ARTICLE?

Welcome to the PF. We do not delete questions that have useful responses.

 

[jedishrfu]

You could share your solution here as this thread will get indexed on Google and other search engines benefitting others studying Landau.

 

[berkeman]

Welcome to the PF. We do not delete questions that have useful responses.

Original post restored in post #1.