Re-writing aircraft equations of motion (attachment problem fixed)

[lucy_b14]

Hi, I hope someone can help me with this question, I originally posted this question in the homework help forumbut no one seems to be able to help me with it. I think my problem is more math related - I don't really know where to start.

I have been a given a matrix containing aircraft equations of motion (see attached picture). Also shown is an equation involving the pilot rudder input (where r is the yawing angular velocity).

Please note: when i looked at the attachment on my computer, the smaller equation didn't display properly until i zoomed in a bit - a minus sign seemed to be missing.

I am asked to rewrite the equation (by 'equation' I think they mean the matrix of equations) showing the pilot’s input only on the right hand side.

I won't attempt to write out all the symbols etc, but my guess at the solution would be to change the top row of the left hand side adding to each column the term -ζ+kr. Though I wouldn't really know what to do about the right hand side - (would the left hand column of the first matrix be deleted - if so that would surely have to change the left hand side of the expression).

Any help with this problem would be much appreciated.

Thanks

 

[Cyrus]

What you have is a state space representation of the equations of motion. Simply expand the equation(s) out by performing the appropriate matrix multiplication. You will have 3 equations when you do this.

Also, you will replace the zetas, with the zeta given by the proportional feedback control law specified at the bottom of your attachment.