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I found an article about swimming in space by deforming one's body. This should not be possible according to my understanding of classical physics, but in curved spacetime it apparently can work.

Now the problem is, I understand how it can be done from the links provided, but I lack the formal mathematical training to make any notion of how fast one could move, or how big one would need to be in order to gain a useful velocity.

The links to the paper, and to a "pop sci" website that explains it with animations

http://dspace.mit.edu/handle/1721.1/6706

http://www.science20.com/hammock_physicist/swimming_through_empty_space

How would I go about calculating this?

Basic calculus (integration by parts etc) and matrix transforms for 3d computer graphics is the limit of my mathematical knowledge.