Discussion Overview
The discussion revolves around finding a simple expression for the angle between two quaternions represented in angle-phase form. Participants explore the mathematical relationships and challenges involved in expressing this angle in terms of the differences in their phase angles.
Discussion Character
- Exploratory
- Technical explanation
- Debate/contested
Main Points Raised
- One participant seeks to express the angle between two quaternions in terms of their phase angles, specifically \(\phi - \phi'\), \(\psi - \psi'\), and \(\theta - \theta'\).
- Another participant suggests using the dot product to find the angle, referencing a resource that discusses calculating angles between quaternions.
- A participant notes that the inner product approach would be more straightforward if the quaternions were in Cartesian form, but expresses difficulty in converting from phase-angle form.
- One reply questions the simplicity of finding such an expression and suggests that the phase-angle form may relate to spherical coordinates.
- Another participant clarifies that the angle used in quaternion calculations may require additional considerations, such as needing a rotation angle for each quaternion.
- References to external resources and code snippets are provided to assist in understanding quaternion relationships and calculations.
Areas of Agreement / Disagreement
Participants do not reach a consensus on a simple solution for expressing the angle between the quaternions. There are multiple competing views and approaches discussed, with some uncertainty regarding the necessary transformations and calculations.
Contextual Notes
Some limitations include the dependence on the definitions of angle-phase form and the challenges in converting to Cartesian coordinates. The discussion also highlights the need for additional parameters, such as rotation angles, which are not fully resolved.