Homework #3
Assigned: Jan. 27th, 2009
Due: Feb. 3rd, 2009
Points: 20

1. 10 points
   (a) Consider two points A and B with coordinates (0,10) and (5,8). Find the curve joining A and B such that its surface of revolution about the x-axis is minimized. Use your solution to write a program (Matlab is easy for this) to plot the curve and give the minimized surface area.
   (b) Now, run your program by lowering the y-coordinate of point B. Plot the minimizing curve in all cases in the same figure (use "hold on" feature in Matlab). Tabulate the minimum surface area against the y-coordinate of B. If you do not see anything interesting happening in doing so, start increasing the x-coordinate of B while fixing the y-cooridnate at as sufficiently low value. Do you see anything interesting now?
2. 10 points
   Use the principle of minimum potential energy for a straight beam and derive the static equilibrium equation; also derive the boundary conditions for all possible end constraints.