A point-mass twin of a rolling body ignores rotational inertia: how wrong are acceleration, slip and coast distance, and what does one calibration fix?

What it found

A frictionless point mass overstates down-ramp acceleration by exactly 1+k (k=I/mr²: 1.4, 1.5, 2.0 for sphere, disc, hoop), so a 2 m descent takes 0.90 s instead of 1.07–1.28 s; a stick/slip simulation matches the closed forms to 3×10⁻⁴ m/s². The slip threshold μ* = k tanα/(1+k) is invisible to the twin, and a launch speed picked in the twin to coast 1 m carries a rolling body 40–100% farther. A gain fitted on one shape removes its own error but leaves −16% to +20% fall-time error on the others (pooled fit +6.7% to −10.7%), and the twin cannot rank the shapes. Stylised: planar incline, Coulomb friction, no rolling resistance or drag, no hardware data.

A figure from its own output

Paper, code and results

• README and method
• White paper
• Experiments and results
• Code
• Tests

More in Digital twins & sim-to-real

• A pinhole twin of a radially distorted camera mis-ranges the near field: how far off does a twin-trained braking policy stop, and does focal calibration fix it?A pinhole twin of a radially distorted camera mis-ranges the floor by exactly 1/(1+k₁h²/R²) (+8.1% at 1 m for k₁=−0.3), a twin-trained braking policy stops 9 cm short of 1 m, focal calibration trades the near-field error for a far-field one, and one grid image identifies k₁.
• An instantaneous-exposure twin of a finite-exposure camera certifies detection at every speed: what is the real speed limit, and what does a blur-matched filter buy back?An instantaneous-exposure twin of a finite-exposure camera certifies detection at every speed; a moving bar is an exact trapezoid (peak C·min(1, w/d)), a twin-tuned peak detector has a hard speed limit wC/(σz), and a blur-matched box filter raises it quadratically (5–55×).
• A twin with an ideal magnetometer returns the true heading: how large is the hard-iron and soft-iron error, what does it do to a compass-held path, and how much of a turn does a swing calibration need?A twin with an ideal magnetometer hides hard/soft-iron heading error: exact peaks asin(β/B) and asin(|1−r|/(1+r)), a compass-held square misses by exactly 2Lβ/B, and swing calibration error grows ×12 at a 90° arc. Stylised.
• A gyro twin calibrated on white noise hides the bias random walk: how wrong are its heading error, re-alignment interval and dead-reckoning budget, and does a single-point Allan fit help?A gyro twin calibrated on white noise hides the bias random walk: heading variance ratio exactly 1+(t/t*)² (2.33 at 100 s, 134 at 1000 s), the twin's re-alignment interval is 24× too long (10 000 s vs 416 s), a single-point Allan fit is right at one horizon only, and dead-reckoning range is over-stated 1.25–1.74×. Stylised.
• A zero-wind twin of a UAV out-and-back leg: does a tailwind repay the headwind, and what does a twin calibrated on one leg say about the return?Zero-wind twin of a UAV out-and-back leg: wind does not cancel (real/twin energy 1/(1−(w/v)²)), the best airspeed moves to v²=w²+√(w⁴+1), and a one-leg-calibrated twin is off by exactly ±w/v with the sign of the leg flown.
• A constant-gain twin of a motor holding a load certifies every load: what does thermal derating do to the real hold?A constant-gain twin of a motor holding a load certifies every load: magnet derating makes holding a positive thermal feedback with a fold at λ=4/27 (real temperature 1.33–2.25× the twin's near it, no hold above it, runaway in ≈4π/(9√ε) thermal time constants), short tests cannot see it, the twin overstates holdable torque 1.1–1.6×, and refitting a constant gain does not remove the fold.

All 164 Digital twins & sim-to-real projects →

Other research topics

Proper scoring & elicitation28Effort & peer prediction9Verification games & slashing19Detection & tolerances14Markets as routers13Prediction-market design9Paying contributors8Decentralised training systems23Digital twins & sim-to-real164LLM chip design loops40Robot manufacturing loops53Ambient AI assistant46Self-replicating manufacturing34Simulation-first design64Engineered clothing45Task-specific AI accelerators40Algorithmic chip-design loops42Open-source purpose-built robots44The software-engineering loop43Adversarial human imitation41Open-source residential construction41Autonomous multi-angle capture34Sensing, imaging and 3D31Energy supply and dense energy storage39Robot societies among people31Agentic co-design of low-cost robots27Laundry-hanging robots25Machine learning on qualitative data23Robots on the building site27Civilizations & group psychology1History & human sciences1

Produced with AI assistance (Claude). Results are from the code in this repository and are simulated or stylised unless the abstract says otherwise; nothing here implies affiliation with or endorsement by any lab, researcher or company cited. MIT licensed.