Coulomb damping¶
Model mechanical energy loss by an approximately constant-magnitude dry-friction force opposing sliding velocity and producing piecewise motion with possible sticking.
Core Idea¶
Coulomb damping is vibration attenuation produced by sliding dry friction idealized as a force of nearly constant magnitude \(F_c=\mu N\) directed opposite instantaneous velocity. For a single-degree-of-freedom oscillator the moving phases may be written \(m\ddot x+kx=-F_c\,\operatorname{sgn}(\dot x)\), with separate conditions at zero velocity. The force law is discontinuous and motion is solved piecewise between reversals.
During each sliding half-cycle, friction removes work equal to its magnitude times distance traveled. Under the ideal constant-force, linear-spring model, successive peak amplitudes decrease by an approximately constant amount rather than the exponential envelope characteristic of viscous damping.
Scope of Application¶
The abstraction is literal wherever practitioners can identify the same constitutive roles, apply the same boundary tests, and obtain the same kind of output. The following habitats are uses of Coulomb damping itself, not metaphors based only on resemblance.
- Vibration analysis. Predicting free-decay envelopes under sliding friction.
- Mechanical joints. Approximating dissipation where interfaces undergo gross slip.
- Isolation devices. Comparing frictional and viscous attenuation models.
- Parameter estimation. Inferring effective friction magnitude from peak decrement.
- Simulation. Handling sign changes and stick conditions with event-aware dynamics.
- Model validation. Checking amplitude and velocity dependence against observed decay.
Clarity¶
A clear account of Coulomb damping must preserve the recognition invariant stated in the Core Idea rather than rely on the title alone. State whether static and kinetic friction are distinguished. Declare the normal-load and constant-magnitude assumptions. Solve between velocity reversals rather than smoothing the sign change silently. Test the predicted constant peak decrement across more than one amplitude range. These declarations are not editorial extras: each changes what observations count, which transformations are licensed, and what conclusion can be drawn.
Manages Complexity¶
Coulomb damping manages complexity by replacing a diffuse field of observations or possible operations with a bounded role structure: sliding interface supplies contact between surfaces supplies dry-friction energy loss.; normal load supplies contact loading scales the ideal friction magnitude.; opposing force supplies force direction reverses with sliding velocity.; restoring dynamics supplies elastic and inertial terms produce oscillatory reversals.; piecewise phases supplies a fixed force sign applies between consecutive zero-velocity events..
Abstract Reasoning¶
- Draw the free-body model and identify the sliding interface. 2. Estimate friction magnitude and direction for each moving phase. 3. Integrate the linear dynamics until the next zero-velocity event. 4. Update force sign or test the static-friction sticking condition. 5. Track frictional work and successive peak amplitudes. 6. Compare predictions against viscous and state-dependent friction alternatives. 7. Retain the law only over the range where its diagnostics hold.
Knowledge Transfer¶
The strict upward abstraction is Damping. Coulomb Damping instantiates Damping because dry-friction work irreversibly removes mechanical energy from motion. Within dry friction vibration, the full mechanism transfers literally when the same roles and boundary tests recur. Beyond that domain, only the parent-level skeleton should travel. Reusing the label Coulomb damping after removing its constitutive vocabulary would hide a change of mechanism behind an analogy. The honest transfer rule is therefore two-stage: recognize the domain-specific pattern first, then lift only the parent relation that remains invariant under a substrate change.
Relationships to Other Abstractions¶
Current abstraction Coulomb damping Domain-specific
Parents (1) — more general patterns this builds on
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Coulomb damping is a kind of Damping Prime
Coulomb Damping instantiates Damping because dry-friction work irreversibly removes mechanical energy from motion.
Hierarchy paths (2) — routes to 2 parentless roots
- Coulomb damping → Damping → Dissipation → Irreversibility → Reversibility and Irreversibility
- Coulomb damping → Damping → Oscillation → Periodicity → Invariance
Neighborhood in Abstraction Space¶
Coulomb damping sits in a sparse region of the domain-specific corpus (99th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.
Family — Unclustered & Miscellaneous (1565 abstractions)
Nearest neighbors
- Traction (mechanics) — 0.78
- Stoneley wave — 0.75
- Fault — 0.74
- Law of the wall — 0.74
- Verlet Integration — 0.73
Computed from structural-signature embeddings · 2026-09-08