Hi All 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>?