Quintuple pendulum
A quintuple pendulum is a string of five pendulums. In this case, we have five pendulums with mass 1 and length 1.
One end of the string of pendulum is fixed. The string is pulled downwords by a gravitational field.
Such a string can be used to model the movement of a physical chain or a rope.
Play with the various buttons. You can fix and then move the end point of the string. After moving this end point, you can release it again to let it swing freely again. Be aware, by moving this end point, the string can become over stressed!
A numerical simulation method is used. The principle idea is as follows: the masses move in accordance with Newton's laws, ie the masses are accelarated downwards. However, their movement is constrained because of the interconnecting rods. The final movement of the masses is the results of a free fall movement minus a correction because of the constraints. The calculation is done by considering a little time interval dt.
Step 1: let all masses move during time interval dt as if there were no constraints (ie no rods). The masses gain a little speed (downwards).
Step 2: Masses on both ends of a rod (a constraint) must have the same speed in the direction of the rod. Because of step 1, the no longer is true. Each constraint results in a correction factor for the velocity.
Step 3: Calculate the new velocities of the masses and from these velocities, update their positions.
Step 4: Go to step 1.
The method used has been described by Etrin Catto (http://box2d.org/files/GDC2009/GDC2009_Catto_Erin_Solver.ppt).