[Script Info]
Title:
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.00,0:00:03.00,Default,,0000,0000,0000,,Now let's try out some of these ideas with the flexible rope.
Dialogue: 0,0:00:03.00,0:00:06.00,Default,,0000,0000,0000,,We'll fix both ends of that rope
Dialogue: 0,0:00:06.00,0:00:11.00,Default,,0000,0000,0000,,and want to see what the equilibrium shape is going to be
Dialogue: 0,0:00:11.00,0:00:13.00,Default,,0000,0000,0000,,under the influence of gravity.
Dialogue: 0,0:00:13.00,0:00:18.00,Default,,0000,0000,0000,,The obvious choice of finite elements is springs.
Dialogue: 0,0:00:18.00,0:00:23.00,Default,,0000,0000,0000,,Springs of a given rest length, so that the potential energy of each spring
Dialogue: 0,0:00:23.00,0:00:29.00,Default,,0000,0000,0000,,amounts to 1/2 times the spring constant times the square of the extension of the spring,
Dialogue: 0,0:00:29.00,0:00:34.00,Default,,0000,0000,0000,,which is the distance between the two endpoints minus the rest length of the string.
Dialogue: 0,0:00:34.00,0:00:40.00,Default,,0000,0000,0000,,To model the mass of that rope, we attach mass points to these strings.
Dialogue: 0,0:00:40.00,0:00:45.00,Default,,0000,0000,0000,,Of course, these mass points carry potential energy due to gravity.
Dialogue: 0,0:00:45.00,0:00:50.00,Default,,0000,0000,0000,,Given the constants that we provide, compute the potential energy of that rope.
Dialogue: 0,0:00:50.00,0:00:55.00,Default,,0000,0000,0000,,The one end of that rope will be fixed at x = 0, y = 0.
Dialogue: 0,0:00:55.00,0:01:05.00,Default,,0000,0000,0000,,The other end of that rope will be fixed at x = 1.3 m and y = 0.4 m.
Dialogue: 0,0:01:05.00,0:01:08.00,Default,,0000,0000,0000,,Our code starts with a random initialization
Dialogue: 0,0:01:08.00,0:01:13.00,Default,,0000,0000,0000,,and then applies a pretty simplistic strategy to minimize the energy.
Dialogue: 0,0:01:13.00,0:01:16.00,Default,,0000,0000,0000,,For a certain number of times it's going to pick one of the masses
Dialogue: 0,0:01:16.00,0:01:20.00,Default,,0000,0000,0000,,and change the position of that mass point by a random vector.
Dialogue: 0,0:01:20.00,0:01:23.00,Default,,0000,0000,0000,,If the energy decreases, it keeps that new position.
Dialogue: 0,0:01:23.00,0:01:26.00,Default,,0000,0000,0000,,If it doesn't, it returns to the position before.
Dialogue: 0,0:01:26.00,9:59:59.99,Default,,0000,0000,0000,,Very simple, but highly inefficient.