Chapter 21 - General Relativity Computational Tools and Conventions for Propulsion
This chapter is about notation, conventions, and computer programs. Math can be long and tedious. While multiplying through by a negative sign is normally not a big deal; physicists, engineers, and mathematicians will be at each other’s throats over which version of an equation is the best (all equations are really different facets of one another). One major difference in notation between physics and math people is in the spherical coordinate system. The zenith angle is phi for math majors and is theta for physics majors. This matters because the roles of phi and theta are switched between the two fields. My personal belief is that theta should be used for the x-y plane (I side with math majors). This is because when using polar coordinates the x-y plane's angle is always called theta. Adding one more dimension shouldn't meaning calling what was theta now phi. However I will use the physics standard, because that is what others in my field are used to.
The book has its own set of recommendations on how to view equations for spacecraft: SI units, positive time-like displacements, more common metric, Riemann tensor through Christoffel symbols, and various other pro space flight beliefs. While there is no preference in terms of software, pros and cons are made available.
Although there are details in the book, the reader of this articles is recommended to research each kind of software themselves. However, the recommended programs for spaceflight (that have been tested so far) are: Maxima, Mathematica, and Maple. These programs each have their own add-ons. Note that there is no perfect piece of software for space applications. I do quite a bit of numerically modeling myself and write my own programs rather than use someone else's stuff so I know exactly what's going on.
People have been attempting to make programs for yet to be discovered things, such as Casimir geometries.