Model, assumptions and workflow · Complete machine-readable evidence
Independent references
The reference imports no production force, derivative or integrator. Four-corner algebra checks slip, rotated forces, track-aware moments and nominal axle equilibrium. A separately derived 2×2 bicycle matrix exponential checks the small-angle transient and equilibrium. Modified midpoint with Richardson extrapolation at 2/4/6/8 substeps supplies an eighth-order nonlinear reference.
Axle cornering stiffness is the sum of its two corner stiffnesses; no additional factor two applies. The equations agree with the lateral/yaw plant described in the MathWorks vehicle dynamics reference.
Budgets fixed before comparison
Force/load/moment algebra: 1e−9 absolute plus 1e−12 relative. Jacobian: 1e−6 plus 2e−6 relative. Small-angle linear limit: 1e−9 plus 1e−4 relative. Nonlinear v/r/heading: 1e−8 SI; world XY: 1e−6 m. Smooth timestep refinement is checked separately from clipped transitions; nonlinear clipping comparisons use 0.0001 s.
Canonical results
135 algebra cases / 540 corners, three linear cases, three nonlinear cases, two smooth convergence cases and 22 invalid-input cases are regenerated by the verification gate. Unit and browser tests additionally cover deterministic transfers, project migrations and applied/draft behavior.
Canonical evidence
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"schemaVersion": "vehiclelab.planar-handling-verification.v1",
"model": {
"id": "vehiclelab.vehicle.planar-handling",
"version": "1.0.0"
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"solver": {
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"version": "1.0.0"
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"algebraRelative": 1e-12,
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"jacobianRelative": 0.000002,
"linearAbsolute": 1e-9,
"linearRelative": 0.0001,
"nonlinearDynamicAbsolute": 1e-8,
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"method": "Independent force algebra, direct lumped-mass equilibrium, analytical 2x2 matrix exponential and eighth-order modified-midpoint extrapolation. Reference imports no production force/derivative/integrator. Fine saturation comparisons use 0.0001 s; smooth RK4 refinement is qualified separately.",
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}What this establishes
This establishes implementation agreement with the declared simplified equations and numerical budgets. It does not establish tire calibration, real-vehicle accuracy, load transfer, integrated chassis controls or any safety qualification.