Classical Mechanics Homework Assignment #8, due by 5 pm Monday October 24 to Krishna’s office Lab 2 3255. All problems from Taylor except as indicated. * indicates problem where MMA might be helpful.
- 6.4
- 6.12
- 6.15
- 6.17
- 6.19
- 6.26
Notes:
- For 6.4, review the discussion on p. 217. This is a famous problem with a famous result; you might already have done a version of this proof in Calculus I as an example of optimization. You won’t use variational methods (other than what is built into Fermat’s Principle already) but you may find yourself using multivariable calculus (specifically partial derivatives).
- For 6.12, make sure to find the actual arsinh function in terms of y and arbitrary integration constants.
- For 6.15, you could use the result of example 6.2 and some cleverness, or you could use this is an opportunity to practice the calculations associated with that famous example. Your choice, or both.
- For 6.19, the area A of the surface of revolution formed by y = y(x) as described is given by the integral of 2πy ds (you can find the explanation of this in a calculus text).
- In problem 6.26, take advantage of this opportunity to solidify your understanding of the steps that take you from equation (6.10) through (6.13).