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Robert Zubrin and Dana Andrews developed the magnetic-sail for use in interplanetary flight and deccelerating from interstellar speeds.

The basic classical equation of motion is this...

V = Vo/(1 + Vo^(1/3)*k*t)^3

...where k is a constant, t is time since decceleration began, Vo is initial velocity, and V final velocity.

It's pretty straight forward to then integrate to find displacement...

s = (1/2k)*(Vo^(2/3)-V^(2/3))

...remembering that V is V(t), a function of t.

Differentiating V(t) gives...

a = -3*Vo^(4/3)*k/(1 + Vo^(1/3)*k*t)^4

...but (V/Vo)^(1/3) = 1/(1+Vo^(1/3)*k*t) so the equation simplifies to...

a = -3*V^(4/3)*k

Those are the basic equations of motion, classically. How would I go about turning them into relativistic equations of motion? Would V(t) need to be rapidity, and t become <tau>?

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# Relativistic motion of a magnetic sail

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