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.

 

[NatSusan]

Hi there,

I'm not sure if I can provide a complete solution, but I can try to give you some guidance on how to approach this problem. First of all, it's great that you recognize that your problem is more math related and that you're having trouble knowing where to start. That's a good first step in solving any problem - identifying where you need help.

From what I understand, you have been given a matrix containing aircraft equations of motion and you need to rewrite the equation so that the pilot's input is only on the right hand side. This means that you need to isolate the pilot's input on one side of the equation and everything else on the other side.

One approach you can take is to use basic algebraic techniques to manipulate the equation. For example, you can try adding or subtracting the same term to both sides of the equation to cancel out certain terms. You can also try multiplying or dividing both sides by the same term to simplify the equation.

In terms of the specific steps you need to take, I'm not sure without seeing the actual equations and matrix. But a general tip is to always start by simplifying the equation as much as possible before trying to isolate the pilot's input. This may involve combining like terms or factoring out common factors.

Also, make sure to pay attention to the signs of each term and be careful when adding or subtracting them. It's possible that the minus sign you mentioned may be causing some confusion, so double check to make sure you're using the correct signs.

I hope this helps and good luck with your problem! Don't hesitate to ask for more specific help if you need it.