How can we use maple seeds for personal transport?

[Cyrus]

The perturbations are a methodology to linearizing (simplifying) the nonlinear equations of motion. They are not inherently a design of any vehicle, the method is used on any/all vehicles, including a Cessna or 737, for example. With the linear model, you can do things like stability analysis and autopilot design. In the example of airspeed I gave above, the delta is not from a gust, its just a deviation from a nominal trim state.

 

[Danger]

Okay, I think that I've got it now. (I'll never understand the field itself, of course, but the explanation makes sense.) Thanks.

 

[boneh3ad]

Wow did this thread take a right turn for the obscure. Haha. From a maple seed aircraft to discussing an advanced, borderline-magical mathematical trick.

 

[Cyrus]

Dude, it's not magic. Honestly, it's straight forward and simple.

 

[boneh3ad]

Multiple scales, for example, is pretty simple. There are other methods that are ridiculously complicated if you want to understand how they actually work. Some of the things in perturbation you just have to take on faith.

For me, multiple scales and matched asymptotic expansions are both not too bad. There are other ones though that were mug more of a black box because they are based on one or two guys' lives' work. Those you had to just kind of take on faith alone.

 

[Cyrus]

Multiple scales, for example, is pretty simple. There are other methods that are ridiculously complicated if you want to understand how they actually work. Some of the things in perturbation you just have to take on faith.

For me, multiple scales and matched asymptotic expansions are both not too bad. There are other ones though that were mug more of a black box because they are based on one or two guys' lives' work. Those you had to just kind of take on faith alone.

I'm talking about replacing states by things like p = p_0 + \delta p and expanding out and dropping terms. Never had to bother with matched asymptotic expansions.

 

[Danger]

Wow did this thread take a right turn for the obscure

It might well be a "right turn" from the original post, but it seems a necessary tool for determining whether or not the machine in question can work.

 

[boneh3ad]

I'm talking about replacing states by things like p = p_0 + \delta p and expanding out and dropping terms. Never had to bother with matched asymptotic expansions.

Then you seemingly haven't been introduced to the formal "perturbation techniques" that I am referring to. Sure introducing disturbances and then canceling out nonlinear terms is easy. That represents about 1% of the battle in the techniques that I was referring to that I had to take a class in. They were pretty brutal.

It might well be a "right turn" from the original post, but it seems a necessary tool for determining whether or not the machine in question can work.

Well I am sure you could make it technically "work." The real question is not "will it work?" but instead "what's the point?" It doesn't offer any benefit over traditional rotary aircraft.

 

[Cyrus]

Then you seemingly haven't been introduced to the formal "perturbation techniques" that I am referring to. Sure introducing disturbances and then canceling out nonlinear terms is easy. That represents about 1% of the battle in the techniques that I was referring to that I had to take a class in. They were pretty brutal.

Yeah, for flight dynamics there isn't that much of a need to do anything more than I described. All we want to do is linearize and obtain the A and B matrices. I can imagine if you're trying to look at something more precise like boundary layer flow it gets more involved. If our models are a bit off it's not a huge issue because the controller has some gain and phase margin built into it to account for plant inaccuracies and disturbance rejection.

 

[boneh3ad]

Yeah, for flight dynamics there isn't that much of a need to do anything more than I described. All we want to do is linearize and obtain the A and B matrices. I can imagine if you're trying to look at something more precise like boundary layer flow it gets more involved. If our models are a bit off it's not a huge issue because the controller has some gain and phase margin built into it to account for plant inaccuracies and disturbance rejection.

Yeah. The point of the ones I have had to use is to take a nonlinear PDE, split it up into n linear PDE's where your accuracy gets better as n increases. That is usually governed by what your small parameter is and the physics of the system. You end up with several equations of increasingly smaller order and you keep as many as you need. Luckily, you don't really need to solve them in my line of work, you just need to extract the information that you need out of it, which is still pretty beastly at times.