https://github.com/inaciovasquez2020/whiplash-stability
Investigation of Whiplash stability effects in model refinement and complexity hierarchies with formal artifacts.
https://github.com/inaciovasquez2020/whiplash-stability
computational-complexity finite-model-theory formal-verification hierarchies refinement stability
Last synced: 2 months ago
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Investigation of Whiplash stability effects in model refinement and complexity hierarchies with formal artifacts.
- Host: GitHub
- URL: https://github.com/inaciovasquez2020/whiplash-stability
- Owner: inaciovasquez2020
- License: other
- Created: 2026-02-20T14:24:19.000Z (4 months ago)
- Default Branch: main
- Last Pushed: 2026-03-22T03:49:15.000Z (3 months ago)
- Last Synced: 2026-04-04T01:37:10.387Z (2 months ago)
- Topics: computational-complexity, finite-model-theory, formal-verification, hierarchies, refinement, stability
- Language: Python
- Homepage: https://inaciovasquez2020.github.io/whiplash-stability
- Size: 23.4 KB
- Stars: 1
- Watchers: 0
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
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README
# Whiplash Stability
Mathematical and computational analysis of stability in high-acceleration or impulsive motion systems (“whiplash” dynamics).
The repository provides modeling tools, numerical experiments, and theoretical notes for analyzing stability of systems subject to rapid changes in acceleration.
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## Core Problem
Consider a dynamical system
x''(t) = F(x(t), x'(t), t)
subject to impulsive or rapidly varying forcing.
The stability objective is to determine conditions under which perturbations δx(t) remain bounded.
Linearized perturbation equation
δx'' = D_x F(x(t), x'(t), t) δx + D_{x'}F(x(t), x'(t), t) δx'
A trajectory is stable if
sup_t ||δx(t)|| < ∞.
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## Repository Structure
src/
core simulation and stability algorithms
notebooks/
numerical experiments and demonstrations
docs/
theoretical derivations and references
tests/
validation of stability conditions
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## Stability Methods
The repository explores several approaches:
1. Lyapunov stability analysis
2. Spectral analysis of linearized dynamics
3. Energy methods for impulsive forcing
4. Numerical integration under high-jerk conditions
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## Example Model
Mass–spring–damper with impulsive forcing
m x'' + c x' + k x = J(t)
where J(t) represents short impulse forces.
Stability condition
c > 0
k > 0
Energy
E(t) = ½ m (x')² + ½ k x²
dE/dt ≤ 0 ensures dissipative stability.
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## Usage
Clone the repository
git clone https://github.com/inaciovasquez2020/whiplash-stability.git
Run simulations
python src/simulate.py
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## Research Goals
- Characterize stability under high-jerk motion
- Provide numerical tools for analyzing impulsive dynamics
- Develop energy-based stability bounds
---
## License
MIT