Critique: Passive Overshoot Artifact (Simulink “Proof”)

Critique and response context for Passive Overshoot Artifact (Simulink “Proof”) in AffineDrift’s control-affine golf-swing framework.

Summary of Concern

The Simulink “Proof of Concept” claims that “Passive momentum contributions can exceed total forces temporarily.” The Weakness: This “overshoot” (where passive force > total force, implying negative/braking input) might be an artifact of the “Skeletal Baseline” having insufficient damping. A real arm/wrist complex has significant viscoelasticity. If the model uses low-friction joints to represent the “Skeleton,” it will swing more wildly (overshoot) than a real passive arm would. Thus, the “negative input” identified might just be the golfer “paying” to emulate the damping that the model forgot to include.

Location

  • Page: articles/affine-nature-golf-swing.qmd
  • Section: Simulink Forward Dynamics Modeling
  • Claim: “Passive momentum contributions can exceed total forces temporarily, indicating competing active and passive effects.”

Nature of the Issue

  • Model Mismatch: Under-damped model \(\rightarrow\) Exaggerated Drift \(\rightarrow\) False “Braking” Input.
  • Interpretation Error: The golfer isn’t “braking” the club; they are just having normal joint viscosity. The model thinks they are braking because the model’s joints are frictionless.

Why This Is a Problem

  • It creates a “Ghost Force”. The taxonomy labels “Viscosity” as “Input” (braking torque).
  • It leads to incorrect coaching advice (“Stop braking the club!”).
  • It invalidates the claim that the Simulink model “validates” the theory. It only validates the math, not the physics.

Evidence / References

  • Winters, J. M. (1990). Hill-based muscle models: A systems engineering perspective. (Passive viscosity is significant).
  • Damping Ratios: Human joint damping ratios are often \(\zeta \approx 0.1 - 0.5\) depending on activation. Steel pin joints are \(\zeta \approx 0.001\).

Severity

  • Medium/High: It biases the numerical results significantly.

Suggested Remedies

  1. Damping Sensitivity Analysis: Run the Simulink model with variable joint damping coefficients (\(b = 0.1, 0.5, 1.0\) Nms/rad).
  2. Conservative Claim: Change “Passive momentum exceeds total” to “Passive momentum component is significant.”
  3. Viscosity Term: Add a specific \(-\Gamma \dot{q}\) term to the Drift field \(f(x)\) to model passive tissue viscosity, separate from the “Skeletal” structure.