Run a physical maneuver
In Studio, choose Test → Advanced analysis → 14-DOF Coupled Transient, then Steering & braking maneuvers (ML-64). Choose zero-rack coast, straight braking, smooth step steer, steering pulse or combined steering and braking. Run creates a complete physical history in Results. Numerical controls and Solver Analysis identify the actual computation.
This generic reference has its own suspension, body and tire parameters. It does not consume the applied Vehicle Assembly, create a 3D motion mapping, or provide ABS, ESC, standstill, emergency stopping or OEM vehicle predictions. Calculations stay in a browser Worker.
Prescribed steering participates in dynamics
The rack coordinate ρ is prescribed alongside the fourteen integrated coordinates q. Its smooth quintic step or out/hold/return pulse supplies position, velocity and acceleration analytically. Every integration stage solves the actual front-left and front-right linkage at current jounce and rack position. Wheel headings, material frames and contact velocities follow that geometry.
The full fifteen-column translational and angular Jacobians form the mass matrix and Newton–Euler bias. The partitioned equations are Mqq q̈ = Qq − bq − Mqρ ρ̈. Bias includes transport, quadratic and mixed velocity terms and gyroscopic effects. The ideal rack and links are massless; this is a prescribed coordinate, not a fifteenth free degree of freedom.
Required rack effort is Mρq q̈ + Mρρ ρ̈ + bρ − Qρ. Rack power is this independently evaluated effort times rack velocity, and is exactly zero for a held rack. It is not inferred from an energy residual. Installed spring and damper rates include rack motion.
Torque, slip and signs
Positive internal relative-rotor torque drives; negative torque brakes. A smooth sin⁴ torque pulse is distributed by four entered fractions summing to one. Wheel speed, current slip, tire forces and vehicle acceleration evolve together. Positive rack displacement initially gives negative front-wheel heading and negative yaw in this particular linkage. Use negative rack for the mirrored positive response.
The accepted ML-63 tire law uses material contact velocity, complete carrier angular velocity and relative rotor spin exactly once. Longitudinal and lateral force demands share the same radial friction disk μFz and the same absolute normal support. There is no commanded deceleration or independent per-axis capacity.
Bounded physical scope
Initial speed is 8–20 m/s and duration is 0.04–1 s. Default studies run 0.6 s with 10 ms stored samples. Rack amplitude is at most ±2 mm with transitions of at least 40 ms; total torque magnitude is at most 400 N m. All stages require four loaded contacts, forward contact transport of 5–25 m/s, slip ratio within ±0.2, slip angle within ±0.15 rad, body-plane wheel heading within ±0.05 rad, attitude within ±0.1 rad and regular jounce travel inside ±40 mm with a derivative margin.
These bounds are checked together. A custom combination can fail before reaching the requested duration. Failure or cancellation never publishes a successful partial history. Zero-loaded-toe mounting is a fixed reference mounting prepared once; the alternative accepted generic mounting retains its physical loaded toe. Held nonzero rack offsets receive their own vertical equilibrium preparation.
Numerical methods and evidence
Classical fixed RK4 and adaptive Dormand–Prince RK45 use the accepted numerical primitives. Both split at every output and input-profile join. Work is integrated at physical stages; damping and tire dissipation have separate ledgers. Stored energy includes kinetic, gravity, installed springs and compliant normal support. The residual is energy change minus rotor and rack work plus damping and tire losses.
The available backend is TypeScript tires plus full moving-mechanism TypeScript mechanics. The existing C++ ABI-v1 backend does not implement this prescribed-coordinate model, so it is not offered here. Bounded Worker execution is research computation and carries no real-time guarantee. Preparation, integration, request, click-to-receipt, RHS counts and integration wall/physical-time ratio are reported separately. Owned channel bytes are not browser-process RAM.
Independent Cartesian geometry, finite-difference material kinematics, projected Newton–Euler equations and a separate extrapolated-midpoint integrator check the moving model. Held-rack reductions check accepted ML-63 behavior; ML-57 comparisons check steering-to-yaw sign only because the formulations and parameters differ. These are mathematical and numerical verification, without experimental tire/vehicle validation or external cross-code correlation.
Read and export actual results
The XY polyline uses stored world coordinates with equal metre scaling on both axes. Its small lateral displacement is not exaggerated; markers and heading arrows use actual samples. Physical plots precede Solver Analysis. CSV retains full-precision SI samples. JSON carries channel units, frames, signs, validity limits, inputs, source and solver identities, diagnostics and negative-zero indices. An interactive run explicitly reports that it has not executed an independent reference.
Each request owns one Worker. Cancel, navigation and project replacement terminate it. Earlier completed evidence remains labelled stale after an unfinished request or input change, with exports disabled. Save/Open preserves the existing project schema; these transient session results are exported separately.
Qualification summary · Full reproducible numerical evidence · Accepted fixed-rack tire coupling