Euler angles in latitude longitude space

In summary, the conversation is discussing the definition of Euler angles in a physics introduction. The individual is questioning how the angles would be defined if a different coordinate system, specifically a latitude, longitude, and proprietary vertical coordinate system, is used. They clarify that the rotations are being performed in curvilinear coordinates, so there is no restriction on the basis vectors being orthonormal.
  • #1
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In most physics introductions Euler angles(pitch, roll, yaw) are defined with respect to Cartesian coordinate system.

If I chose not to use a Cartersian coordinate system but instead use a latitude, longitude and a proprietary vertical coordinate(and no back transformations to Cartersian coordinate system permitted) basis vector space how would the pitch, yaw, roll Euler angles be defined ?

What I mean by this is the following

Initially I have a point defined in terms of λ,∅ and the vertical coordinate is defined as ζ.

Now I rotate the axes (not the point !) to a new set of axes λ',∅',ξ'.

I want to be able to define the Euler angles with respect to these two sets of orthonormal vectors.
 
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  • #2
I want to correct what I wrote yesterday. When a proprietary vertical coordinate is used there is no restriction of basis vectors being orthonormal. These are basically curvilinear coordinates in which the rotations are being performed.
 

FAQ: Euler angles in latitude longitude space

1. What are Euler angles in latitude longitude space?

Euler angles in latitude longitude space are a way of representing the orientation of an object or coordinate system in three-dimensional space. They consist of three angles - typically called pitch, roll, and yaw - which describe the rotation around each of the three axes of the coordinate system.

2. How are Euler angles related to latitude and longitude?

While Euler angles can be used to describe the orientation of any three-dimensional object, they are often used in the context of navigation and mapping. In this case, the pitch and yaw angles correspond to changes in latitude and longitude, respectively, while the roll angle represents changes in altitude or elevation.

3. What is the difference between Euler angles and other coordinate systems?

Euler angles are just one way of representing the orientation of an object in three-dimensional space. Other popular coordinate systems include quaternions and rotation matrices. The main difference between these systems is the number of parameters required to fully specify the orientation - for example, quaternions require four parameters while Euler angles only require three.

4. How are Euler angles calculated?

The calculation of Euler angles depends on the specific coordinate system being used. In general, the angles can be determined by considering the rotations around each of the three axes, starting with the first rotation (typically pitch), then the second (roll), and finally the third (yaw). The exact formulas for calculating the angles vary depending on the chosen coordinate system.

5. What are some applications of Euler angles in latitude longitude space?

Euler angles in latitude longitude space have a wide range of applications, including navigation and mapping, aircraft and spacecraft control, robotics, and computer graphics. They are also commonly used in geodesy and cartography for describing the orientation of the Earth's surface and for creating three-dimensional maps and models.

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