Sunday, December 7, 2014

Left Turn at Andromeda, Cont'd

The title of my last post was a reference to the old Bugs Bunny cartoons in which Bugs says, "I knew I shoulda taken that left turn at Albuquerque." Here are some further thoughts on the two problems.

First, the problem of getting back to the origin with a velocity vector rotated 90 degrees. How long will it take, using a constant-thrust accelerator?

Measured in appropriate units of time, the 45-45-90 solution takes around 3.68 ticks of the clock:



Those slowdowns at the corners are painful to watch; one can do better. The best I'm able to do is \(\sqrt{10}\approx 3.16\) ticks of the clock:



Here is a side-by-side comparison:



As for the second problem, making the left turn without having to return to the origin first, the best I can do is \(\sqrt{4+2\sqrt{2}} \approx 2.61\) ticks of the clock:



If anyone can do either problem faster, let me know!

In the meantime, here's a supercut of Bugs Bunny:


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