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.

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.

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 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.

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 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 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.