% Workshop Example 9  (WorkshopEx09.m)
%
% This program determines the equilibrium positions of
% the three linked bungee jumpers based on minimizing
% the potential energy.

% Daniel D. Warner
% November 7, 2008
clear
clc

% Set up the parameters of the Bungee Jumper problem
echo on
% The weights for Alex, Barry, and Carol (in pounds)
wA = 225;
wB = 160;
wC = 105;
w = [wA wB wC]';

% The lengths of the bungee cords (in feet)
L = [15 15 15]';

% The bungee cord spring constants (in lbs/ft)
C = diag([75 30 30]);

% Set up the structural matrix, A.  This is the matrix
% that defines the elongations given the displacements
% e = A*x
A = [1 0 0; -1 1 0; 0 -1 1]

% Calculate the stiffness matrix.
K = A'*C*A

% Calculate the displacements that minimize the potential
% energy of this system.
% That is, solve Equation 9 from the Workshop Handout
x = K \ w

% Calculate the potential energy of this system.
p = 0.5*x'*K*x - x'*w

% Calculate z, the equilibrium positions of the jumpers.
e = A*x
z = A \ (e+L)

echo off