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Topic:
Misner, Thorne and Wheeler, Exercise 8.5 (c)
Replies:
38
Last Post:
Apr 13, 2013 11:57 PM




Re: Misner, Thorne and Wheeler, Exercise 8.5 (c)
Posted:
Apr 7, 2013 11:34 PM


"Hetware" wrote in message news:AuGdnVu7TbVslv_MnZ2dnUVZ_g6dnZ2d@megapath.net...
This is the geodesic equation under discussion:
d^2(r)/dt^2 = r(dp/dt)^2
d^2(p)/dt^2 = (2/r)(dp/dt)(dr/dt).
r is radius in polar coordinates, p is the angle, and t is a path parameter.
The authors ask me to "[S]olve the geodesic equation for r(t) and p(t), and show that the solution is a uniformly parametrized straight line(x===r cos(p) = at+p for some a and b; y===r sin(p) = jt+k for some j and k).
I tried the following:
(d^2(p)/dt^2)/(dp/dt) = (2/r)(dr/dt)
f=dp/dt
(df/dt)/f = (2/r)(dr/dt)
1/2 ln(f) + k = ln(r)
a(f^(1/2)) = r
a(dp/dt)^(1/2) = r
And substitute for r in:
d^2(r)/dt^2 = r(dp/dt)^2
to get
d^2(r)/dt^2 = a(dp/dt)^(3/2)
But there I'm stuck.
How should the problem be handled? ============================================= What you have is a second order differential equation. Unlike the solution to the general polynomial equation, ax +bx^2 + cx^3 + ... + kx^n = 0, where you seek a value for x given values for a,b,c etc., the solution for a differential equation is a FUNCTION. In other words you cannot obtain a numerical or algebraic value (you don't have enough information and that is not the idea anyway) but you can find functions r(t) and p(t) . The authors have already told you the solution is a straight line, which is of course a function. http://search.snap.do/?q=solving+differential+equations&category=Web HTH, because we don't do homework for you.
 This message is brought to you from the keyboard of Lord Androcles, Zeroth Earl of Medway. When the fools chicken farmer Wilson and Van de faggot present an argument I cannot laugh at I'll retire from usenet.


Date

Subject

Author

4/7/13


Guest

4/7/13


Lord Androcles, Zeroth Earl of Medway

4/8/13


Lord Androcles, Zeroth Earl of Medway

4/8/13


Hetware

4/8/13


Lord Androcles, Zeroth Earl of Medway

4/8/13


Hetware

4/9/13


Lord Androcles, Zeroth Earl of Medway

4/9/13


Hetware

4/8/13


Hetware

4/8/13


Lord Androcles, Zeroth Earl of Medway

4/9/13


Hetware

4/9/13


Lord Androcles, Zeroth Earl of Medway

4/9/13


Hetware

4/9/13


Lord Androcles, Zeroth Earl of Medway

4/9/13


Hetware

4/8/13


Dirk Van de moortel

4/8/13


Lord Androcles, Zeroth Earl of Medway

4/8/13


rotchm@gmail.com

4/9/13


Dirk Van de moortel

4/13/13


Dono

4/13/13


rotchm@gmail.com

4/13/13


Dono

4/13/13


Dono

4/13/13


Dono

4/13/13


rotchm@gmail.com

4/13/13


Dono

4/13/13


rotchm@gmail.com

4/13/13


Dono

4/13/13


Dono

4/13/13


rotchm@gmail.com

4/13/13


Dono

4/13/13


rotchm@gmail.com

4/13/13


Dono

4/9/13


Guest

4/9/13


Dirk Van de moortel

4/9/13


Lord Androcles, Zeroth Earl of Medway

4/8/13


Rock Brentwood

4/8/13


Hetware

4/8/13


Lord Androcles, Zeroth Earl of Medway


