Ah, my apologies, I must not have worded it clear enough. I'll try again.
So I'm not making an actual model, it's purely theoretical. I've considered a wing from an aircraft, and I want to express it in the form shown in the picture above. My only unknown is the spring constants, which I'm...
Greetings Good People,
As the title suggests, I'm having some trouble getting to a 2D model. The process is to select an aircraft (or wing model), and model it as a 2D, 2DOF wing-tunnel model.
The aircraft I selected was a Cessna 172. This had a tapered wing, which after some calculations and...
Okay, I think I was able to do it. For the sake of completion, I'll put the rest of my solution here.
I realize the substitution probably wasn't necessary, but I found it easier to do thinking about it that way.
Thank you very much everyone for all your help :)
This is just not making any sense, sorry. I'll put all the steps I've done below.
I feel like I'm just going in circles. And then for:
Depending on which way I do it, I get different answers... which is weird! I don't get it.
Yeah, I don't know anymore, nothing is working
I'll try write out how I got it as soon as I can. For now, when multiplying that out, I get ##e^{i\theta}-e^{-i\theta}##
Ah, that is a mistake on my part. Though I don't suppose ##e^{i\theta-i\alpha}## would make it correct
Hello. Thanks for your replies, much appreciated. I tried again following your advice, and I couldn't eliminate ##2θ##. This is what I ended up with:
$$=U_{\infty}\frac{e^{i\theta+i\alpha}-e^{i\alpha-i\theta}+2\sin(\alpha)i}{e^{2i\theta}}$$
Well actually, this was one way of writing it. The...
Greetings.
I'm having a bit of difficulty with getting from the first to the second equation. I know some basic identities, but it all just feels like a mess. My approach was just going to be to write whatever I could, but some of the terms are confusing me...
My apologies, maybe I should have actually listened and shared the rest of the solution. I sort of get what you're doing there, and recognise two formulas from the z-transform table. This is the rest of the solution:
Could it possibly be that the statement, 'Noting that the poles in the...
That's the solution as I saw it; everything after is using the inverse z-transform. And I agree, I still have absolutely no clue what complex conjugates have to do with this
Wow, uh. Right you are, my apologies. That's quite embarrassing lol
THAT is what I meant to say! Seems I've got it all muddled up. Thanks a lot Mark, that's made it quite clear how that fraction is split.
Okay... that makes sense. But then the next part:
How can you just split a fraction like that? For example:
$$\frac{x+y}{z}=\frac{x}{z}+\frac{y}{z}$$
You can do that. But what you can't do is:
$$\frac{x+y}{w+z}=\frac{x}{w+z}+\frac{y}{w+z}$$
So how come it's being done there? Is there something...
So the original question is from Control Theory, and the topic is the inverse z-transform. This is a part from the solution I just can't understand. The reason it has to be in this form (##z^{-1}##) is because that's the form used in the z-transform table. The question essentially is, how do you...