Refactor: eliminate quaternion derivative code duplication in u_dot_generalized_3dof

[Copilot]

Pull request type

• Code maintenance (refactoring, formatting, tests)

Checklist

• All tests (pytest tests -m slow --runslow) have passed locally

Current behavior

The quaternion derivative calculation in u_dot_generalized_3dof had identical code blocks duplicated in two places (lines 1958-1962 and 1989-1993):

# Block 1: Normal misalignment case
e0_dot = 0.5 * (-omega1_wc * e1 - omega2_wc * e2 - omega3_wc * e3)
e1_dot = 0.5 * (omega1_wc * e0 + omega3_wc * e2 - omega2_wc * e3)
# ... same formulas

# Block 2: Anti-aligned case (duplicated)
e0_dot = 0.5 * (-omega1_wc * e1 - omega2_wc * e2 - omega3_wc * e3)
e1_dot = 0.5 * (omega1_wc * e0 + omega3_wc * e2 - omega2_wc * e3)
# ... same formulas again

New behavior

Refactored to compute omega_body first in all branches, then calculate quaternion derivatives once:

• First: Determine omega_body based on alignment state (normal, anti-aligned, or aligned/None)
• Then: Compute quaternion derivatives in a single block if omega_body is not None

This reduces maintenance burden—formula updates only need to happen in one place.

Breaking change

• No

Additional information

Addresses code review feedback on PR #883.

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[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 80.39%. Comparing base (b1eb6cb) to head (c92d5f0).
⚠️ Report is 1 commits behind head on enh/3-dof-lateral-motion-improvement.

Additional details and impacted files

@@                           Coverage Diff                            @@
##           enh/3-dof-lateral-motion-improvement     #903      +/-   ##
========================================================================
- Coverage                                 80.91%   80.39%   -0.52%     
========================================================================
  Files                                       107      106       -1     
  Lines                                     13486    13043     -443     
========================================================================
- Hits                                      10912    10486     -426     
+ Misses                                     2574     2557      -17     

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[Gui-FernandesBR]

Could separate the whole function into smaller methods... It makes code more readable and prevents refactors like this.

[aZira371]

Could separate the whole function into smaller methods... It makes code more readable and prevents refactors like this.

@Gui-FernandesBR separating the whole u_generalized_3dof function ? maybe yes that can be done like can create a separate helper function which does the whole wc thing. I saw your comment after merging. Will add a TODO for it, can take this up later. But will keep the advice in mind.