Rewriting aircraft equations of motion

[lucy_b14]

Hi, I hope someone can help me with this question, although its aeronautical engineering, I think I have more of a maths related problem - 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

 

[KataKoniK]

Hello,

First of all, it's great that you are seeking help with this problem. It's always important to reach out and ask for assistance when you are stuck on a problem.

Based on the information provided, it seems like you have been given a matrix of equations that describe the aircraft's motion, as well as an equation involving the pilot's rudder input. Your task is to rewrite this equation, showing the pilot's input only on the right hand side.

To accomplish this, you will need to manipulate the matrix of equations. As you mentioned, you can start by adding the term -ζ+kr to the top row of the left hand side. This will account for the pilot's input in the equations.

Next, you will need to address the right hand side of the equation. This will involve deleting the left hand column of the first matrix, as you suggested. However, this will also require you to change the left hand side of the expression. This is because the left hand side represents the aircraft's motion without the pilot's input, while the right hand side represents the effect of the pilot's input on the aircraft's motion.

To make this change, you can add the left hand column of the first matrix to the right hand side of the equation. This will ensure that the left hand side remains unchanged, while the right hand side now only includes the pilot's input.

I hope this explanation helps you to better understand how to approach this problem. Remember to always take your time and think through each step carefully when working on mathematical problems. Good luck!

 

[Mene]

I would suggest approaching this problem by first understanding the physical meaning of the equations of motion and the role of the pilot's input in controlling the aircraft. This will help in identifying the relevant parameters and their relationships in the equations.

Next, I would suggest breaking down the equations into smaller, more manageable parts and studying each part individually. This will help in understanding the structure of the equations and how they are connected.

Once a thorough understanding of the equations is achieved, I would recommend using mathematical techniques, such as substitution and rearranging, to manipulate the equations and rewrite them in the desired form.

It is also important to carefully consider the units and dimensions of the variables in the equations to ensure that the rewritten equations are physically meaningful.

Furthermore, consulting with experts in the field of aeronautical engineering or mathematics can provide valuable insights and guidance in approaching this problem.

In summary, rewriting aircraft equations of motion requires a combination of understanding the physical principles, breaking down the equations, and applying mathematical techniques. With persistence and careful consideration, the desired solution can be achieved.