Added qprop.

qprop.m

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+function q = qprop(q, w, dt)
+
+% QPROP  Quaternion propagation
+%
+% Discretely propagates a quaternion via its average rotation rate over a
+% time step.
+% 
+%    q = QPROP(q, w, dt)
+% 
+% This function is vectorized to operate on numerous quaternions and 
+% rotation rates simultaneously.
+%
+% Input:
+%
+% q   Quaternion to propagate (scalar last) (4-by-1 or 4-by-n)
+% w   Rotation rate (rad/s) (3-by-1 or 3-by-n)
+% dt  Time step (s) (scalar or 1-by-n)
+%
+% Output:
+%
+% q   Propagated quaternion (4-by-1 or 4-by-n)
+% 
+
+% Copyright 2016-2017 An Uncommon Lab
+
+%#codegen
+
+    [w, w_mag] = normalize(w);       % Rot. unit vector and speed
+    w_mag      = 0.5 * w_mag .* dt;  % Half rotation angle
+    swm        = sin(w_mag);
+    qr         = [swm .* w(1,:); ... % Rotation quaternion
+                  swm .* w(2,:); ...
+                  swm .* w(3,:); ...
+                  cos(w_mag)];
+    q          = qcomp(qr, q);       % Updated quaternion
+
+end % qprop

todo.txt

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+Test qprop.