VER-TRA-001 · PASS

Free Translational Motion

This case verifies the SDF translational propagation path under zero acceleration against the analytical solution of uniform rectilinear motion.

Open mathematical model Back to Verification

Verification Objective

The case isolates translational state propagation from gravity, propulsion, coordinate transformations, and rotational dynamics. A controlled physics model returns exactly zero acceleration while the production SDF physics façade and Euler integration path propagate position and velocity.

VerifiedTranslational propagation path

ReferenceClosed-form analytical solution

FrameInertial translational state vectors

AutomationGoogleTest + CTest

Mathematical Reference

With zero translational acceleration, $\dot{\mathbf{v}} = 0$ , velocity remains constant.

\mathbf{v}(t) = \mathbf{v}_0

Position therefore follows uniform rectilinear motion:

\mathbf{r}(t) = \mathbf{r}_0 + \mathbf{v}_0 t

This is a useful first verification case because the analytical solution is exact and the expected state can be determined independently of the SDF implementation.

Reference Configuration

Initial position{ 1000, -2000, 3000 } m

Initial velocity{ 10, -5, 2 } m/s

Acceleration{ 0, 0, 0 } m/s²

Time step0.1 s

Duration10.0 s

Integration steps100

Expected Final State

\mathbf{v}(10\,s) = (10, -5, 2)\;\mathrm{m/s}

\mathbf{r}(10\,s) = (1100, -2050, 3020)\;\mathrm{m}

Position tolerance1e-9 m

Velocity tolerance1e-12 m/s

SDF Execution Path

Initial state→ZeroAccelerationModel→physics::computePos / computeVel→EulerIntegrator→Analytical comparison

The controlled acceleration model is a test double. The propagation itself uses the production SDF physics façade and numerical integrator, so the case verifies the software path that advances the translational state without introducing unrelated model effects.

Result

PASS

VER-TRA-001 matches the analytical reference.

The final position and velocity remain within the defined numerical tolerances after 100 deterministic integration steps.

Start 3: VER_TRA_001_FreeTranslation.MatchesAnalyticalSolution
3/3 tests passed
100% tests passed, 0 tests failed

Scope of Evidence

Passing VER-TRA-001 demonstrates correct propagation of free translational motion for this bounded reference case. It does not verify lunar gravity, thrust generation, coordinate transformations, rotational dynamics, or the complete spacecraft simulation. Those behaviors require separate verification cases.

Review the translational motion model