# Numerical integration RK4 for the given data

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I have the angular veocity data shown below and wanted to apply , where.

w

Columns 1 through 9

5.0468 0.1049 -0.1582 -0.4549 -0.7088 -0.8615 -0.8758 -0.7409 -0.4740

3.2405 0.6230 0.6264 0.5425 0.3348 0.0279 -0.3276 -0.6692 -0.9351

-0.0000 -0.0049 -0.0119 -0.0229 -0.0369 -0.0526 -0.0687 -0.0837 -0.0962

Columns 10 through 18

-0.1169 0.2715 0.6264 0.8889 1.0163 0.9908 0.8218 0.5447 0.2142

-1.0766 -1.0664 -0.9047 -0.6183 -0.2562 0.1194 0.4448 0.6665 0.7518

-0.1053 -0.1100 -0.1100 -0.1053 -0.0962 -0.0837 -0.0687 -0.0526 -0.0369

Columns 19 through 22

-0.1062 -0.3561 -0.4855 5.7553

0.6957 0.5261 0.3291 1.6874

-0.0229 -0.0119 -0.0049 -0.0000

%The skew matrix is given by

W= [ 0,-w(1),-w(2),-w(3);

w(1), 0, omg(3),-w(2);

w(2),-w(3), 0, w(1);

w(3), w(2),-w(1), 0];

Apperciated !

##### 6 Comments

James Tursa
on 18 Aug 2020

James Tursa
on 18 Aug 2020

Edited: James Tursa
on 18 Aug 2020

What are the units of your sampled w? Those numbers look way too large for rad/sec.

### Accepted Answer

James Tursa
on 18 Aug 2020

Edited: James Tursa
on 18 Aug 2020

E.g., a VERY SIMPLISTIC approach showing one step of Euler integration

dt = some delta time value

q = [1,0,0,0]; % Initial quaternion, scalar first

w = a 1x3 angular rate vector in rad/sec from your sampled data

qdot = 0.5 * quatmultiply( q, [0 w] ); % Assuming right chain convention

q = q + qdot * dt; % One Euler step

This is just to show a very basic idea. In practice, one would use more sophisticated methods of integration.

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