% A minimal chaotic system: two beads on a short string, pinned at both
% ends, free to move in 3D (6 degrees of freedom). Struck hard and
% off-axis, the motion is chaotic: turn on "perturbed twin" to run it again
% with the strike changed by one part in 1e9 and watch the two runs
% separate exponentially until they are unrelated. Scale the strike down
% (try 0.025) and the motion is regular: the separation grows only slowly.
%
% Transverse modes at small amplitude: sqrt(f0/(m*a))/(2*pi) * [1, sqrt(3)]
% = 159 and 276 Hz.

a = 0.01;          % bead spacing (m)
m = 1e-4;          % bead mass (kg)
f0 = 1;            % string tension (N)
strain = 0.05;     % spring stretch at rest

[pos, E] = bp_chain(4, 3 * a);
sys.pos = pos;
sys.mass = m;
sys.pinned = [1 4];
sys.springs = bp_springs(pos, E, f0 / (strain * a), f0);
% every mode falls 60 dB in 2.5 s
sys = bp_decay(sys, [200 2.5]);

s = 1;                         % strike strength; try 0.025 for regular motion
hit.beads = 2;
hit.velocity = s * [12 6 40];  % m/s, off-axis
sys.hits = hit;

sys.listen = struct('beads', 3, 'dir', [0 0 1]);
sys.duration = 3;
sys.dt = 1 / (48000 * 8);   % the automatic step is set at rest; the hard strike
                             % needs a finer one to keep energy drift small