Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math.independent

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Guest

Watch Watch this User
Re: Misner, Thorne and Wheeler, Exercise 8.5 (c)
Posted: Apr 9, 2013 12:40 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On 4/8/2013 9:27 AM, Dirk Van de moortel wrote:
> Hetware <hattons@speakyeasy.net> wrote:
>> 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).

>
> Normally we'd write dotted variables, but with quotes it's easier.
> So write


Like this?

<math xmlns='http://www.w3.org/1998/Math/MathML'
mathematica:form='TraditionalForm'
xmlns:mathematica='http://www.wolfram.com/XML/'>
<mrow>
<mrow>
<mover>
<mi>r</mi>
<mo>..</mo>
</mover>
<mo>=</mo>
<mrow>
<msup>
<mrow>
<mi>r</mi>
<mo>&#8289;</mo>
<mo>(</mo>
<mover>
<mi>&#981;</mi>
<mo>&#183;</mo>
</mover>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>=</mo>
<mi>r</mi>
</mrow>
</mrow>
<mo>&#8291;</mo>
<msup>
<mi>&#969;</mi>
<mn>2</mn>
</msup>
</mrow>
</math>
<math xmlns='http://www.w3.org/1998/Math/MathML'>
<mtext>

</mtext>
</math>
<math xmlns='http://www.w3.org/1998/Math/MathML'
mathematica:form='TraditionalForm'
xmlns:mathematica='http://www.wolfram.com/XML/'>
<mrow>
<mrow>
<mi>r</mi>
<mo>&#8290;</mo>
<mover>
<mi>&#969;</mi>
<mo fontweight='bold'>&#183;</mo>
</mover>
</mrow>
<mo>=</mo>
<mrow>
<mrow>
<mo>-</mo>
<mn>2</mn>
</mrow>
<mo>&#8290;</mo>
<mi>&#969;</mi>
<mo>&#8290;</mo>
<mover>
<mi>r</mi>
<mo fontweight='bold'>&#183;</mo>
</mover>
</mrow>
</mrow>
</math>
<math xmlns='http://www.w3.org/1998/Math/MathML'>
<mtext>
</mtext>
</math>
<math xmlns='http://www.w3.org/1998/Math/MathML'
mathematica:form='TraditionalForm'
xmlns:mathematica='http://www.wolfram.com/XML/'>
<mrow>
<mrow>
<mfrac>
<mover>
<mi>r</mi>
<mo>..</mo>
</mover>
<mi>r</mi>
</mfrac>
<mo>=</mo>
</mrow>
<mo>&#8291;</mo>
<msup>
<mi>&#969;</mi>
<mn>2</mn>
</msup>
</mrow>
</math>
<math xmlns='http://www.w3.org/1998/Math/MathML'>
<mtext>

</mtext>
</math>
<math xmlns='http://www.w3.org/1998/Math/MathML'
mathematica:form='TraditionalForm'
xmlns:mathematica='http://www.wolfram.com/XML/'>
<mrow>
<mfrac>
<mover>
<mi>&#969;</mi>
<mo fontweight='bold'>&#183;</mo>
</mover>
<mi>&#969;</mi>
</mfrac>
<mo>=</mo>
<mrow>
<mrow>
<mo>-</mo>
<mn>2</mn>
</mrow>
<mo>&#8290;</mo>
<mfrac>
<mover>
<mi>r</mi>
<mo fontweight='bold'>&#183;</mo>
</mover>
<mi>r</mi>
</mfrac>
</mrow>
</mrow>
</math>
<math xmlns='http://www.w3.org/1998/Math/MathML'>
<mtext>
</mtext>
</math>
<math xmlns='http://www.w3.org/1998/Math/MathML'
mathematica:form='TraditionalForm'
xmlns:mathematica='http://www.wolfram.com/XML/'>
<mrow>
<mrow>
<mi>ln</mi>
<mo>&#8289;</mo>
<mo>(</mo>
<mi>&#969;</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mrow>
<mrow>
<mrow>
<mo>-</mo>
<mn>2</mn>
</mrow>
<mo>&#8290;</mo>
<mrow>
<mi>ln</mi>
<mo>&#8289;</mo>
<mo>(</mo>
<mi>r</mi>
<mo>)</mo>
</mrow>
</mrow>
<mo>+</mo>
<mi>k</mi>
</mrow>
</mrow>
</math>
<math xmlns='http://www.w3.org/1998/Math/MathML'>
<mtext>

</mtext>
</math>
<math xmlns='http://www.w3.org/1998/Math/MathML'
mathematica:form='TraditionalForm'
xmlns:mathematica='http://www.wolfram.com/XML/'>
<mrow>
<mrow>
<mi>&#969;</mi>
<mo>=</mo>
<mi>a</mi>
</mrow>
<mo>&#8291;</mo>
<msup>
<mi>r</mi>
<mrow>
<mo>-</mo>
<mn>2</mn>
</mrow>
</msup>
</mrow>
</math>
<math xmlns='http://www.w3.org/1998/Math/MathML'>
<mtext>
</mtext>
</math>
<math xmlns='http://www.w3.org/1998/Math/MathML'
mathematica:form='TraditionalForm'
xmlns:mathematica='http://www.wolfram.com/XML/'>
<mrow>
<mfrac>
<mi>&#969;</mi>
<mi>a</mi>
</mfrac>
<mo>=</mo>
<msup>
<mi>r</mi>
<mrow>
<mo>-</mo>
<mn>2</mn>
</mrow>
</msup>
</mrow>
</math>
<math xmlns='http://www.w3.org/1998/Math/MathML'>
<mtext>
</mtext>
</math>
<math xmlns='http://www.w3.org/1998/Math/MathML'
mathematica:form='TraditionalForm'
xmlns:mathematica='http://www.wolfram.com/XML/'>
<mrow>
<msqrt>
<mfrac>
<mi>&#969;</mi>
<mi>a</mi>
</mfrac>
</msqrt>
<mo>=</mo>
<msup>
<mi>r</mi>
<mrow>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msup>
</mrow>
</math>
<math xmlns='http://www.w3.org/1998/Math/MathML'>
<mtext>
</mtext>
</math>
<math xmlns='http://www.w3.org/1998/Math/MathML'
mathematica:form='TraditionalForm'
xmlns:mathematica='http://www.wolfram.com/XML/'>
<mrow>
<mrow>
<mover>
<mi>r</mi>
<mo>..</mo>
</mover>
<mo>=</mo>
<msqrt>
<mfrac>
<mi>a</mi>
<mi>&#969;</mi>
</mfrac>
</msqrt>
</mrow>
<mo>&#8291;</mo>
<msup>
<mi>&#969;</mi>
<mn>2</mn>
</msup>
</mrow>
</math>


Date Subject Author
4/7/13
Read Misner, Thorne and Wheeler, Exercise 8.5 (c)
Guest
4/7/13
Read Re: Misner, Thorne and Wheeler, Exercise 8.5 (c)
Lord Androcles, Zeroth Earl of Medway
4/8/13
Read Re: Misner, Thorne and Wheeler, Exercise 8.5 (c)
Lord Androcles, Zeroth Earl of Medway
4/8/13
Read Re: Misner, Thorne and Wheeler, Exercise 8.5 (c)
Hetware
4/8/13
Read Re: Misner, Thorne and Wheeler, Exercise 8.5 (c)
Lord Androcles, Zeroth Earl of Medway
4/8/13
Read Re: Misner, Thorne and Wheeler, Exercise 8.5 (c)
Hetware
4/9/13
Read Re: Misner, Thorne and Wheeler, Exercise 8.5 (c)
Lord Androcles, Zeroth Earl of Medway
4/9/13
Read Re: Misner, Thorne and Wheeler, Exercise 8.5 (c)
Hetware
4/8/13
Read Re: Misner, Thorne and Wheeler, Exercise 8.5 (c)
Hetware
4/8/13
Read Re: Misner, Thorne and Wheeler, Exercise 8.5 (c)
Lord Androcles, Zeroth Earl of Medway
4/9/13
Read Re: Misner, Thorne and Wheeler, Exercise 8.5 (c)
Hetware
4/9/13
Read Re: Misner, Thorne and Wheeler, Exercise 8.5 (c)
Lord Androcles, Zeroth Earl of Medway
4/9/13
Read Re: Misner, Thorne and Wheeler, Exercise 8.5 (c)
Hetware
4/9/13
Read Re: Misner, Thorne and Wheeler, Exercise 8.5 (c)
Lord Androcles, Zeroth Earl of Medway
4/9/13
Read Re: Misner, Thorne and Wheeler, Exercise 8.5 (c)
Hetware
4/8/13
Read Re: Misner, Thorne and Wheeler, Exercise 8.5 (c)
Dirk Van de moortel
4/8/13
Read Re: Misner, Thorne and Wheeler, Exercise 8.5 (c)
Lord Androcles, Zeroth Earl of Medway
4/8/13
Read Re: Misner, Thorne and Wheeler, Exercise 8.5 (c)
rotchm@gmail.com
4/9/13
Read Re: Misner, Thorne and Wheeler, Exercise 8.5 (c)
Dirk Van de moortel
4/13/13
Read Re: Misner, Thorne and Wheeler, Exercise 8.5 (c)
Dono
4/13/13
Read Re: Misner, Thorne and Wheeler, Exercise 8.5 (c)
rotchm@gmail.com
4/13/13
Read MTW, Exercise 8.5 (c), Crotchm reasserts his imbecility
Dono
4/13/13
Read MTW Exercise 8.5 (c) - Crotchm the poser puts his foot in his mouth,
big time
Dono
4/13/13
Read Re: Misner, Thorne and Wheeler, Exercise 8.5 (c)
Dono
4/13/13
Read Re: Misner, Thorne and Wheeler, Exercise 8.5 (c)
rotchm@gmail.com
4/13/13
Read Re: Misner, Thorne and Wheeler, Exercise 8.5 (c)
Dono
4/13/13
Read Re: Misner, Thorne and Wheeler, Exercise 8.5 (c)
rotchm@gmail.com
4/13/13
Read Re: Misner, Thorne and Wheeler, Exercise 8.5 (c)
Dono
4/13/13
Read Re: Misner, Thorne and Wheeler, Exercise 8.5 (c)
Dono
4/13/13
Read Re: Misner, Thorne and Wheeler, Exercise 8.5 (c)
rotchm@gmail.com
4/13/13
Read MTW Exercise 8.5 (c) - Crotchm the poser puts his foot in his mouth,
big time
Dono
4/13/13
Read Re: MTW Exercise 8.5 (c) - Crotchm the poser puts his foot in his
mouth, big time
rotchm@gmail.com
4/13/13
Read Re: MTW Exercise 8.5 (c) - Crotchm the poser puts his foot in his
mouth, big time
Dono
4/9/13
Read Re: Misner, Thorne and Wheeler, Exercise 8.5 (c)
Guest
4/9/13
Read Re: Misner, Thorne and Wheeler, Exercise 8.5 (c)
Dirk Van de moortel
4/9/13
Read Re: Misner, Thorne and Wheeler, Exercise 8.5 (c)
Lord Androcles, Zeroth Earl of Medway
4/8/13
Read Re: Misner, Thorne and Wheeler, Exercise 8.5 (c)
Rock Brentwood
4/8/13
Read Re: Misner, Thorne and Wheeler, Exercise 8.5 (c)
Hetware
4/8/13
Read Re: Misner, Thorne and Wheeler, Exercise 8.5 (c)
Lord Androcles, Zeroth Earl of Medway

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.