How to Integrate Kepler's Problem in Landau Mechanics?

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Discussion Overview

The discussion revolves around the integration of Kepler's problem as presented in Landau Mechanics, specifically focusing on the equations of motion and the constants involved, such as angular momentum, mass, and mechanical energy. The scope includes theoretical aspects of mechanics and integration techniques.

Discussion Character

  • Technical explanation, Homework-related

Main Points Raised

  • One participant seeks assistance on how to integrate Kepler's problem as outlined in Landau Mechanics.
  • Another participant suggests using integral tables to find a similar integral, indicating that this approach is acceptable for complex integrals.
  • A third participant claims to have solved the problem and expresses a desire to delete their initial post, indicating a possible misunderstanding of the forum's policy on question deletion.
  • Further replies encourage sharing the solution for the benefit of others, emphasizing the value of maintaining useful discussions.

Areas of Agreement / Disagreement

There is no consensus on the integration method, as participants have offered different approaches and suggestions without resolving the initial query.

Contextual Notes

The discussion does not clarify specific assumptions or methods for integrating Kepler's problem, nor does it address any unresolved mathematical steps related to the integration process.

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

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

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

How to integrate it?
Please help me...
 

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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.
 
physicophysiologist said:
I SOLVED IT
HOW CAN I DELETE THIS ARTICLE?
Welcome to the PF. We do not delete questions that have useful responses.
 
You could share your solution here as this thread will get indexed on Google and other search engines benefitting others studying Landau.
 
Last edited:
berkeman said:
Welcome to the PF. We do not delete questions that have useful responses.
Original post restored in post #1.
 

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