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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

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Investigation of Whiplash stability effects in model refinement and complexity hierarchies with formal artifacts.

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# 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

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## License

MIT