MTW Gravitation Electronic Notebook

[rayj]

TL;DR

Options for electronic notebooks to exercise equations in general relativity using notation of MTW G.

I would like to exercise the formulations in the book. I have read Gravitation and many others but I need to do more exercises. I get very bogged down in writing out the symbols. Are there electronic solutions for writing and exercising these equations? I have used Mathcad to perform algebraic equations. I would love to be able to do this as a companion to MTW G.

Any suggestions?

 

[jedishrfu]

Perhaps look to cosmoslogical simulation software.

I found this one called EAGLE but not sure where you can get the code or even what programming language and support libs are used.

http://icc.dur.ac.uk/Eagle/

language wise you might find some code for Julia which is being used in a lot of computational projects.

 

[rayj]

jedishrfu

That was a great site with wonderful information.

Yes, there is the possibility of obtaining code for calculations.

My primary concern is to be able to perform the symbolic math.

 

[jedishrfu]

Most real-world simulations of complex systems do not yield analytical solutions (ie a symbolic solution won't be available) only numerical ones. The simplest case of the three-body problem is one:

https://en.wikipedia.org/wiki/Three-body_problem

As you an see, there are solutions that while quite beautiful, are not analytical but can be computed numerically. Introductory courses often use this system to help the student understand the best algorithms to choose based on whether the system is periodic or not.

All numerical ODE algorithms introduce some form of error that manifests itself as energy added or removed from the system. The trick for a periodic system is to choose an algorithm that adds some error and then takes away some error periodically allowing the solution to stay stable longer.

In the course I took, the prof had us swap in different ODE algorithms. In some cases, the planets spiraled into each other, in other cases they flew apart.