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

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 Hetware Posts: 148 Registered: 4/13/13
Re: Misner, Thorne and Wheeler, Exercise 8.5 (c)
Posted: Apr 8, 2013 11:50 PM

On 4/8/2013 12:58 AM, Lord Androcles, Zeroth Earl of Medway wrote:
> "Hetware" wrote in message
> news:EIednTlOU8ji2v_MnZ2dnUVZ_o6dnZ2d@megapath.net...
>
> 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,
> =====================================================
> SR and GR are codswallop, so it is scarcely surprising if 99%
> of posts to sci.physics.relativity are codswallop.
> The video you cited is also codswallop. This is much better:
>

The English translation: