This is laying out the system of equations for aircraft flight. It is using a reference frame of stationary with respect to the aircraft to make the calculations easier. This is a very common reference frame for setting up equations of motion because it can, in many cases make the math a whole lot easier. This is especially true for a rotating frame or a spherical frame. The Earth happens to be both.
Once the equations of motion are laid out in one reference frame they can be described in any reference frame using a transformation matrix that describes the transformation (changing the point of view of the equations) to the reference frame of choice.
In this starting case, the reference frame is one where the earth is flat and non-rotating. To translate it to another reference frame, such as a spherical rotating reference frame one would run the equations in this document through a transformation matrix that described such a change of reference frame. The resulting equations btw would be a nightmare, but laying them out in this easier reference frame first, makes life a whole lot easier for people to communicate with each other.
If someone STARTED their paper with the equations in a spherical rotating reference frame and it was my job to read their paper I would leave my office, go down to the author's office and shoot them, just so that they would hire someone else.
That's not what I said at all. But yes, I do. Being able to read math (or really in this case physics) is just like reading any other language. It takes time and practice to learn it.
Without spending too much time making sure this is the right thing (I'd have to make sure of all the equations in the NASA paper you referenced, which is FAR too much time), I believe the transformation matrix you are looking for is on page 30 of this powerpoint.
I picked that up immediately. In engineering, calculations are sometimes simplified by 'nullifying' them out or disregarding it when not a factor. After all the report is about a 'Linear' aircraft model.
so... they had to take into account the curvature of the earth when engineering the golden gate bridge, but they can just safely ignore the curvature of the earth when trying to land an airplane? seems legit.
Bridge design is not linear and is distantly related to "linear" aircraft model as you are to a detritus rock..... Well, may be not. Nevertheless, the designs are radically different and take into consideration very different forces. Did you read linear in the title? Do you understand linear? Why would it include "linear" aircraft model, if they were going to consider non-linear considerations?
As I said, to change it to a rotating spherical reference frame you take the equations of motion in the Euclidian frame (flat, non-rotating) and transform them into the new reference frame (spherical rotating) using the appropriate transformation matrix.
I apologize if this doesn't make any sense to you, but just to show you what I'm talking about: Transformation Matrix.
Your snarky rhetoric does not strengthen your position, it just proves that you don’t understand the physics and math involved.
There are people here with degrees in physics, engineering and mathematics telling you what this means, but no, I’m sure your degree in music appreciation is just as valid to evaluate this stuff, right?
Read further. Explains why these models assume no atmosphere or gravitational forces. This doesn't prove what you think it does.
To elaborate a little bit:
This is laying out the system of equations for aircraft flight. It is using a reference frame of stationary with respect to the aircraft to make the calculations easier. This is a very common reference frame for setting up equations of motion because it can, in many cases make the math a whole lot easier. This is especially true for a rotating frame or a spherical frame. The Earth happens to be both.
Once the equations of motion are laid out in one reference frame they can be described in any reference frame using a transformation matrix that describes the transformation (changing the point of view of the equations) to the reference frame of choice.
In this starting case, the reference frame is one where the earth is flat and non-rotating. To translate it to another reference frame, such as a spherical rotating reference frame one would run the equations in this document through a transformation matrix that described such a change of reference frame. The resulting equations btw would be a nightmare, but laying them out in this easier reference frame first, makes life a whole lot easier for people to communicate with each other.
If someone STARTED their paper with the equations in a spherical rotating reference frame and it was my job to read their paper I would leave my office, go down to the author's office and shoot them, just so that they would hire someone else.
hmm, so what you are saying is that pilots are too stupid to understand the math, but you do?
That's not what I said at all. But yes, I do. Being able to read math (or really in this case physics) is just like reading any other language. It takes time and practice to learn it.
yeah, it took me a couple of years to do the math...
most people can't get past question 4 without resorting to a thought-terminating cliche
https://i.redd.it/g287hbmcb94z.png
Kek.
Your argument lacks, care to explain? I already know. Anyone with eyes to see soon will too. Especially if this is the best plug for all these leaks.
Please see my response about changing reference frames above. It does not "lack".
You can't reference your claimed matrix calculations or any curvature calculations. I understand.
You didn't ask.
Without spending too much time making sure this is the right thing (I'd have to make sure of all the equations in the NASA paper you referenced, which is FAR too much time), I believe the transformation matrix you are looking for is on page 30 of this powerpoint.
I picked that up immediately. In engineering, calculations are sometimes simplified by 'nullifying' them out or disregarding it when not a factor. After all the report is about a 'Linear' aircraft model.
so... they had to take into account the curvature of the earth when engineering the golden gate bridge, but they can just safely ignore the curvature of the earth when trying to land an airplane? seems legit.
Bridge design is not linear and is distantly related to "linear" aircraft model as you are to a detritus rock..... Well, may be not. Nevertheless, the designs are radically different and take into consideration very different forces. Did you read linear in the title? Do you understand linear? Why would it include "linear" aircraft model, if they were going to consider non-linear considerations?
As I said, to change it to a rotating spherical reference frame you take the equations of motion in the Euclidian frame (flat, non-rotating) and transform them into the new reference frame (spherical rotating) using the appropriate transformation matrix.
I apologize if this doesn't make any sense to you, but just to show you what I'm talking about: Transformation Matrix.
our advanced calculations are far too difficult for mere mortals to understand, so just take our word for it.
Your snarky rhetoric does not strengthen your position, it just proves that you don’t understand the physics and math involved.
There are people here with degrees in physics, engineering and mathematics telling you what this means, but no, I’m sure your degree in music appreciation is just as valid to evaluate this stuff, right?
this 30 second NASA video debunks your moon landing myth
https://youtu.be/9HQfauGJaTs?t=8s
people weight less at the equator than they do at the poles, because of centrifugal force, right?
No, because they are a little further from the center of mass, because the earth is not perfectly round, it bulges at the equator.
It's funny how quickly a little thinking can produce so many plot holes.