Calculation record
Third variations of the actual curvature integral by Taylor arithmetic.
This independent differentiation avoids cancellation in finite differences.
The polynomial variable is a geometric variation parameter, not a fitted
particle-field magnitude. Both spatial normal directions are retained.
Research context
- Nonlinear response of the bending modes
The same surface curvature energy that gives simplex frequencies has nonzero canonical mode couplings, an exact quadratic resonance and a scale response that must enter any nonlinear particle fixed point.
- Diagnostic catalog
Reproduction commands and scope descriptions for every local finite diagnostic and helper.
Interpret numerical checks within the assumptions and limitations documented in these notes.