HW3 Hints - PHYS 3202 Classical Mechanics II - Homework #3...

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PHYS 3202 Classical Mechanics II - Homework #3 Additional Hints Problem 1. Part 1- The circle is r = constant , z = another constant in the cylindrical coordinate system. See Appendix F.2 of Thornton and Marion, 5th Edition for information about the cylindrical coordinate system. You will need Equation (F.7) for the length element of a path. The time it takes light to travel a tiny distance ds is dt = ds v , where v ( r ) = c/n ( r ) is the local speed of light at distance r from the z -axis. Part 2- If you get two equations involving z 0 ( φ ) and r 0 ( φ ), you can solve them for z 0 and r 0 in terms of r . The resultant equation for r 0 can then be solved by an integral. The following formula may be useful: Z dr r 1 - B 2 - A 2 r 2 = C + 1 1 - B 2 ln r 1 - B 2 + 1 - B 2 - A 2 r 2 . After you find r ( φ ), try to simplify it as much as possible. The hyperbolic func- tions will be very useful when simplifying your results. Search for hyperbolic func- tions at http://en.wikipedia.org/ , or go to Appendix D.6 of Thornton and Marion,
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This note was uploaded on 01/22/2012 for the course PHYS 3202 taught by Professor Tan during the Spring '11 term at Georgia Institute of Technology.

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HW3 Hints - PHYS 3202 Classical Mechanics II - Homework #3...

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