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rpmc

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Apologies up front for the long question … I have tried to be brief.

I want to define camera angles for Google Earth (GE) when rotated about an aircraft yaw axis. The input is Latitude, Longitude, Altitude plus

However, I want to be able to rotate the GE camera view around the aircraft yaw axis by some arbitrary angle, and derive new GE Heading, Tilt, and Roll angles that would replicate, for example, looking left instead of straight ahead. At any point in time, the aircraft can be turning or performing aerobatics including inverted flight, and I want the rotated GE Heading, Tilt, and Roll angles to capture the aircraft maneuvering. For example, an aircraft performing an inside loop looks like a left barrel roll to a camera pointing -90 degrees Yaw = left. As I understand the camera rotation, it is an intrinsic rotation relative to the current aircraft axis system. The answer I need, the rotated GE angles, must be stated relative to the world coordinate system.

Assumptions:

Aircraft Relative to World, right handed system

Roll axis = x, roll angle = u

Pitch axis = y, pitch angle = v

Yaw axis = z, yaw angle = w (positive Z = down)

Camera relative to Aircraft, right handed system

Roll axis = xx, roll angle = a

Pitch axis = yy, pitch angle = b

Yaw axis = zz, yaw angle = c (positive zz = belly of plane)

I understand the elemental rotation functions are:

and similar for the camera rotation about the airplane axis system.

What next? I think my first problem is to generate the correct full rotation matrix that is a product of the elemental extrinsic rotations of the aircraft times the product of the elemental intrinsic rotations of the camera. Is that correct? I believe I'm having difficulty keeping track of extrinsic vs. intrinsic and producing the final, full rotation matrix. And, I may indeed be wrong about the first rotation being extrinsic.

After that, the issue is to find the GE rotated Heading, Tilt and Roll angles that come out of the final full rotation matrix.

Any suggestions or links to references are most appreciated. I would like to accomplish this first using Euler (Tait-Bryan) rotations, and after I understand that, move on to Quaternions.

Robert

I want to define camera angles for Google Earth (GE) when rotated about an aircraft yaw axis. The input is Latitude, Longitude, Altitude plus

**Heading, Pitch and Bank**angles, actually coming from Flight Simulator. These drive the GE camera view which is similarly defined in terms of Latitude, Longitude, Altitude and**Heading, Tilt and Roll angles**, with the GE camera initially looking straight ahead, along the roll axis of the aircraft. As I understand it, these angles define an extrinsic rotation (is this correct?) relative to the world coordinate system, but at any rate, they are supplied by Flight Simulator. This part is working fine and I get a GE view the pilot would see looking straight ahead.However, I want to be able to rotate the GE camera view around the aircraft yaw axis by some arbitrary angle, and derive new GE Heading, Tilt, and Roll angles that would replicate, for example, looking left instead of straight ahead. At any point in time, the aircraft can be turning or performing aerobatics including inverted flight, and I want the rotated GE Heading, Tilt, and Roll angles to capture the aircraft maneuvering. For example, an aircraft performing an inside loop looks like a left barrel roll to a camera pointing -90 degrees Yaw = left. As I understand the camera rotation, it is an intrinsic rotation relative to the current aircraft axis system. The answer I need, the rotated GE angles, must be stated relative to the world coordinate system.

Assumptions:

Aircraft Relative to World, right handed system

Roll axis = x, roll angle = u

Pitch axis = y, pitch angle = v

Yaw axis = z, yaw angle = w (positive Z = down)

Camera relative to Aircraft, right handed system

Roll axis = xx, roll angle = a

Pitch axis = yy, pitch angle = b

Yaw axis = zz, yaw angle = c (positive zz = belly of plane)

I understand the elemental rotation functions are:

Code:

```
Rx(u)= 1 0 0
0 c(u) -s(u)
0 s(u) c(u)Ry(v)= c(v) 0 s(v)
0 1 0
-s(v) 0 c(v)Rz(w)= c(w) -s(w) 0
s(w) c(w) 0
0 0 1
```

and similar for the camera rotation about the airplane axis system.

What next? I think my first problem is to generate the correct full rotation matrix that is a product of the elemental extrinsic rotations of the aircraft times the product of the elemental intrinsic rotations of the camera. Is that correct? I believe I'm having difficulty keeping track of extrinsic vs. intrinsic and producing the final, full rotation matrix. And, I may indeed be wrong about the first rotation being extrinsic.

After that, the issue is to find the GE rotated Heading, Tilt and Roll angles that come out of the final full rotation matrix.

Any suggestions or links to references are most appreciated. I would like to accomplish this first using Euler (Tait-Bryan) rotations, and after I understand that, move on to Quaternions.

Robert

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