## 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: