Math 641-600 Extra Problems
Extra Problems on the Calculus of Variations.
- These problems are from the text.
- Problem 2, page 206 (§ 5.1).
- Problem 6, page 207 (§ 5.1).
- Problem 7, page 207 (§ 5.1).
- Hanging chain problem. A chain having uniform linear density
ρ hangs between the points (0,0) and (1,0). The total mass m,
which is fixed, and the total energy E of the chain are
Assuming that the chain hangs in a shape that minimizes the
energy, find the shape of the hanging chain.
Posted 12/7/05 (fjn).