Description
Remember, x is dummy variable. You may need to write the functions you are minimizing as
dependent on z, ✓, etc. For example, in problem 2 you are minimizing a z0
(✓). The goal is to solve
for z.
1: (medium) – Minimize R x2,y2
x1,y1
ds Where ds = p
dx2 + dy2. This is longer if you fail to notice
what d f
dx = 0 implies. Use equation 6.18 to find the solution.
The solution is that y=Ax+B. Essentially you are showing that the shortest path between two points in two dimensions is a straight
line.
2: (medium) – Minimize the path along the surface of a circular cylinder of radius R. Essentially,
minimize p
dx2 + dy2 + dz2 where R is constant. remember x = Rcos(✓) and y = Rsin(✓).
Write the
function that you are minimizing as F(z(✓)). Show that your answer describes a helix. Use equation
6.18 again.