Sam, numerical stability

I spent the train ride coming back from Queen's drafting an AAS obituary about Roweis. I decided also that I am going to count scientific reminiscence about Roweis as research for the purposes of this diary, lest I end up with nothing to say!

On the flight back to New York, I followed up an intuition floating around in my head that small changes in what we call the orbital parameters could make the code that converts between phase-space position and standard orbital elements much more numerically stable at edge cases. I found some nice things, and I am confident that there are large improvements to be made. Here's a trivial example: Instead of working with inclination of the orbit and the longitude of the ascending node, work with the sine of the first times the sine and cosine of the second. These two products are just the x and y components of the angular-momentum-direction unit vector. A well-known change is to work with the argument of perihelion plus the longitude of the ascending node and not with argument on its own, but I think I can show that an even better one is to work with the eccentricity times the sine and cosine of that angle sum. And so on. Not sure if we will analyze and implement all these before or after we finish our Holmes project.

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