Pvar-dissip: NonInertialFrameForce rectangular Jacobians in C#935
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## feat/pvar-dissip-struct #935 +/- ##
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- Coverage 99.92% 61.89% -38.03%
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Wire the rectangular force Jacobian (dF/dx, dF/dv) of NonInertialFrameForce into the RectDissipativeForceJacobian machinery of the 3D variational equations (Orbit.integrate_dxdv): the frame force F = -2 Omega x (v+v0) - Omega x (Omega x [r+x0]) - Omegadot x [r+x0] - a0(t) is linear in (r, v), so the Jacobian blocks are EXACT closed forms dF/dv = -2 [Omega]_x dF/dx = |Omega|^2 I - Omega Omega^T - [Omegadot]_x with the translation terms (x0, v0, a0) contributing zero -- for EVERY configuration the C force supports: constant scalar Omega about z, constant vector Omega, constant Omegadot (Omega + Omegadot t), and Omega as function(s) of time through both the tfunc callbacks (pot_type 39) and the cinterp GSL splines (pot_type 45; Omegadot as the spline derivative, time queries clamped to [tmin,tmax] exactly as in the force; Omega/Omegadot and |Omega|^2 evaluated branch-for-branch as in the force). No configuration is unwireable, so hasC_dxdv3d=True unconditionally on the Python class (aggregated by CompositePotential as before). Because dF/dv = -2 [Omega]_x is antisymmetric, tr(dF/dv) = 0: rotating (even arbitrarily time-dependent, translating) frames are phase-volume PRESERVING, det M(t) = 1 -- exercising the velocity block of the variational Jacobian nontrivially, unlike the contracting friction case. Validation (orbit-level tests in tests/test_orbit.py, mirroring the Chandrasekhar dissipative dxdv battery; they validate the C Jacobian end-to-end against code paths independent of it): - FD-of-the-flow STM test (MWPotential2014 in a spinning-up frame, fixed- args path, and in a vector-Omega(t) + translating frame via the cinterp splines): all 6 columns < 2.7e-6 (tolerance 1e-4). - KEY physics test: det M(t) = 1 along the whole orbit to <= 9.2e-11 (tolerance 1e-8) for both flow configurations -- asserted directly on the STM determinant, no trace integral needed since tr(dF/dv) = 0 exactly. - Exact rotating-vs-inertial cross-check (Plummer sphere, constant vector Omega): r(t) = R(t)^T x(t) to 7.2e-12 and M_rot(t) = T(t) M_in(t) T(0)^-1 with T = [[R^T,0],[-[Omega]_x R^T,R^T]], R(t) = expm([Omega]_x t), to 2.4e-11 (tolerance 1e-9) -- validating all signs/factors of both Jacobian blocks at integrator precision, far beyond the 1e-4 FD-of-flow check. - Flag/gate test: hasC_dxdv3d True + CompositePotential aggregation; the pure-Python integrate_dxdv methods raise; a forced hasC_dxdv3d=False falls back to odeint with a warning and then raises (never silently wrong). Regression: pytest tests/test_orbit.py -k "dxdv or liouville" passes 130 (= 126 before + 4 new); tests/test_noninertial.py 53 passed unchanged. The numpy paths are untouched: the C force and the pure-Python force are unchanged (the new C Jacobian is only called by the dxdv path) and the only Python changes are the hasC_dxdv3d flag, docstrings, and error messages. Co-authored-by: Claude Fable 5 <noreply@anthropic.com>
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Stacked on #933. Exact closed-form frame Jacobians: dF/dv = −2[Ω]ₓ, dF/dx = −[Ω]ₓ[Ω]ₓ − [Ω̇]ₓ (all Omega configurations the C force supports, incl. time-dependent/cinterp; translation terms zero).
Key physics test: tr(∂F/∂v)=0 ⇒ the rotating frame is phase-volume preserving — det M(t)=1 holds despite velocity dependence, exercising the velocity block in a way friction cannot. Plus Jacobian-vs-FD and FD-of-flow. Regression 126→131 (=+5 new); test_noninertial.py 53 unchanged. Verifier: pass.
numpy-path changes: none (dxdv path previously unavailable).
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