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Hetware
Posts:
148
Registered:
4/13/13


Re: Misner, Thorne and Wheeler, Exercise 8.5 (c)
Posted:
Apr 8, 2013 12:28 AM


On 4/8/2013 12:07 AM, Lord Androcles, Zeroth Earl of Medway wrote: > "Lord Androcles, Zeroth Earl of Medway" wrote in message > news:Njr8t.334633$Ic.40149@fx07.fr7... > > "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. > > ================================ > Hetware's silence is deafening. > We should all be poised at the ready to answer his questions > immediately instead of sleeping in bed when he writes them. > >  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.
Do you realize how much codswallop is posted to this newsgroup in comparison to actual relevant content? Oh well, whatever, nevermind....http://www.youtube.com/watch?v=pkcJEvMcnEg


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


