BUG: correct the position-vector convention in u_dot_generalized

[thc1006]

u_dot_generalized reads two Rocket attributes as vectors from the center of dry mass, and both of them run the other way. Addresses #1186.

Pull request type

• Code changes (bugfix, features)

Checklist

• Tests for the changes have been added (if needed)
• Docs have been reviewed and added / updated
• Lint (ruff check / ruff format --check, pylint) has passed locally
• All tests have passed locally
• CHANGELOG.md: one line, since the workflow that would have written it has not run since CI: run the changelog job for pull requests from forks #1112 (BUG: the changelog workflow stopped running, and CHANGELOG.md is 37 merged pull requests behind #1173).

Current behavior

The v1 derivation takes the center of dry mass as its origin, so it wants a vector from the CDM to the instantaneous center of mass and one from the CDM to the nozzle exit. The two attributes it reads are defined the other way round:

• evaluate_com_to_cdm_function documents the identity com_to_cdm_function + center_of_mass == center_of_dry_mass_position, which makes it CM to CDM, and it labels its own output "Z Coordinate COM to CDM".
• nozzle_to_cdm is -(nozzle_position - center_of_dry_mass_position) * _csys, which is nozzle to CDM.

u_dot_generalized uses both without negating them, so r_CM and r_noz point the wrong way and the moment arm they form has the wrong sign. lateral_surface_wind, in the same file, does negate com_to_cdm_function before using it as a vector from the CDM, so the file is not consistent with itself.

New behavior

Both are negated where the derivation reads them, and the v_dot term that carries r_CM ^ w_dot changes sign with them.

docs/technical/equations_of_motion_v1.rst now states which origin it works in and that the two attributes are the opposite vectors, so the next reader does not have to infer it. Several typos in the derivation go with it: r_CM where the term is r_CM' or r_CM'', a missing plus before the aerodynamic force, the sign on the gravity term of T21, a square dropped from the H matrix and a brace misplaced around another.

Breaking change

• Yes

Simulation results move. Nothing in the API changes, but any number that comes out of the generalized equations is different, so a study built on the old ones will not reproduce.

Additional information

The acceptance flight moves toward the measurement rather than away from it. tests/acceptance/test_defiance_rocket.py carries MEASURED_APOGEE_AGL = 9308.32 from the 2024 Defiance flight:

	apogee AGL	error against the measurement
develop at a50d07d5	9243.8350 m	0.6928 %
with this change	9247.9733 m	0.6483 %

I would not read one flight as proof on its own. It is one data point, and it is the only measured one in the suite.

What the new tests pin. tests/unit/simulation/test_generalized_eom.py is seven tests against a stand-in rocket, among them that the angular acceleration uses a lever arm measured from the center of mass, that an axial force through the axis produces no rotation, that the result does not depend on which reference origin the same physical setup is described in, and that the block system the documentation states is the one the code solves. Putting each half of the change back turns exactly the tests that half is about red, and leaves the rest green: the CM vector un-negated takes down six, the nozzle vector un-negated takes down the one named after it, and the v_dot sign alone takes down the reference-origin and block-system tests.

Expectations that move. Four parametrised values in tests/unit/simulation/test_flight.py change at apogee_time; that file says its expected values were copied from a run rather than derived, and are expected to change on a bug fix. The Defiance impact point moves further than the 3 m the acceptance test allows, so its two references follow the flight, x from 1609.40 to 1550.23 and y from 87.03 to 104.80. Max speed and max acceleration stay inside the 1 percent that test gives them.

Verified on a50d07d5:

pytest tests/                       2655 passed, 10 failed
  the same on develop a50d07d5      2644 passed, 10 failed
ruff check . / ruff format --check  clean
pylint rocketpy/ tests/ docs/       10.00/10, exit 0

The ten are the same ten on both, all of them optional dependencies this machine does not have.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 91.58%. Comparing base (a50d07d) to head (927e771).

Additional details and impacted files

@@             Coverage Diff             @@
##           develop    #1196      +/-   ##
===========================================
- Coverage    91.58%   91.58%   -0.01%     
===========================================
  Files          132      132              
  Lines        18404    18403       -1     
===========================================
- Hits         16855    16854       -1     
  Misses        1549     1549              

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