/sci/ - Science & Math

[Anonymous No.1773389]

Having some difficulty in my astrophysics course.

2) If a relativistic rocket has a proper acceleration alpha that
increases with proper time tau according to:
alpha(tau) = 2/[Cosine(tau)^2 - Sine(tau)^2]
find its motion, r(t), from the point of view of a control tower
for whom the rocket is motionless at r(0) = 0.
(Hint: alpha(tau) here is the derivative with respect to tau of
ln[tan(tau + pi/4)] .)

I've got it down to:

(1-B)/2 = cos[t*(sqrt(1-B^2)+pi/4]^2

B = v/c.

I'm stuck trying to solve for B (Beta). Once I get B, I can figure out r(t).

[Anonymous No.1773521]

Using a power reduction formula and a pi/2 shift, I've gotten it to:

B-1 = sin(2*t*sqrt(1-B^2))
B=v/c

How do I solve for r(t)?