How many solver iterations does a physics twin need to hold a stack of boxes still?

What it found

A from-scratch projected Gauss-Seidel (sequential-impulse) contact solver at 60 Hz on a 1-D stack of n unit boxes starting at rest, checked against the exact static contact impulses. The iterations per step needed to hold the stack (speed under 1 mm/s, total overlap under 0.1 mm, and for every larger count tried) grow faster than n: 1 at n = 2, 8 to 16 at n = 4, 64 to 128 at n = 6, 128 to 512 at n = 12, and over 2048 for n = 16 (bottom-up warm start) or n = 32 (every variant). Sixteen iterations hold at most 4 boxes. More iterations do not reliably help: at n = 16, 1024 holds and 2048 does not. Cold start needs more at small n and is mixed at large n; sweep order has no clean rule. One-dimensional, normal force only, one step size and Baumgarte factor, no real engine run; the cause of the non-monotone behaviour is not isolated.

A figure from its own output

Paper, code and results

• README and method
• Experiments and results
• Tests

More in Digital twins & sim-to-real

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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.