Solving D'Inverno Ch 19 Problem 19.5

  • Thread starter TerryW
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In summary, TerryW is struggling with problem 19.5 in Chapter 19 of D'Inverno. They have successfully worked out components of gab and Jab for the cartesian frame but are having trouble with the transformations into spherical coordinates. Specifically, they are unable to get satisfactory results for g'10, g'11, and g'13. Despite trying different approaches, they cannot find where the discrepancy is coming from. The problem involves applying multiple transformations to obtain a specific form, and TerryW is asking for any ideas or suggestions to help solve it.
  • #1
TerryW
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Has anyone worked all the way through D'Inverno Chapter 19 Problem 19.5?

I've had a good thrash at it - it is quite a bit of work, but I haven't been able to get to a satisfactory conclusion. I've worked out all the components of gab and Jab (for the cartesian frame) but when when I work through the transformations into the spherical co-ordinates, I get the correct answers for g'00, g'02, g'03, g'12, g'22, g'23 and g'33. The results for g'10, g'11, g'13 just will not come out with results that let me work through to the end of the problem successfully. The result for g'12 is fine and for this I used all the components of g'ab and Jab (except for g00) which is trivial.

In the case of g'10, my result has a divisor of (r2+a2), but I've worked through two different ways to find that the answer probably ought to have a divisor of Δ. I just cannot see where this can come from given the values for gab and Jab.

Any ideas anyone?


Regards

TerryW
 
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  • #2
Would you mind posting the problem?
 
  • #3
Hi Elfmotat,

I've a pdf with the relevant information from pages 251 and 252 of D'Inverno. The problem is as follows:

Apply the transformation (19.29) to (19.28) and then the transformation (19.24) to the result, to obtain the form (19.27).

Clearly the answer to part 1 is going to be something like (19.22). I used this idea to 'reverse engineer' g'01 leaving me with two expressions which were the same apart from a term which is r2 + a2 when I do the transformation and Δ (as defined by(19.26) when I do the 'reverse engineer'.

I'm going to see what happens if I replace r2 + a2 with Δ in (19.28), Maybe you can spot what is going wrong.

Regards


TerryW
 

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1. How do I approach solving D'Inverno Ch 19 Problem 19.5?

In order to solve this problem, it is important to carefully read and understand the problem statement. Then, break down the problem into smaller parts and identify any relevant equations or principles that may be applicable. It may also be helpful to draw diagrams or make lists to organize the information. Finally, work through the problem step by step, checking your work and making sure to show all calculations.

2. What is the purpose of solving D'Inverno Ch 19 Problem 19.5?

The purpose of solving this problem is to apply the principles and concepts learned in D'Inverno's 19th chapter to a specific scenario. It allows for the practical application of knowledge and the development of problem-solving skills.

3. How long does it typically take to solve D'Inverno Ch 19 Problem 19.5?

The amount of time it takes to solve this problem will vary depending on individual understanding and problem-solving abilities. It is important to take the time needed to fully understand and solve the problem, rather than rushing through it.

4. What should I do if I get stuck while solving D'Inverno Ch 19 Problem 19.5?

If you get stuck while solving this problem, it can be helpful to take a break and come back to it with a fresh perspective. You can also try working through the problem with a classmate or consulting with a teacher or tutor for guidance. It is important to seek help when needed and not to get discouraged.

5. What are some tips for successfully solving D'Inverno Ch 19 Problem 19.5?

Some tips for successfully solving this problem include carefully reading and understanding the problem statement, organizing information and using relevant equations or principles, showing all calculations, and double-checking your work. It can also be helpful to practice problem-solving on similar types of problems in order to improve your skills.

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