{"id":47878454,"url":"https://github.com/inaciovasquez2020/whiplash-stability","last_synced_at":"2026-04-04T01:37:12.952Z","repository":{"id":339606307,"uuid":"1162649220","full_name":"inaciovasquez2020/whiplash-stability","owner":"inaciovasquez2020","description":"Investigation of Whiplash stability effects in model refinement and complexity hierarchies with formal 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impulsive motion systems (“whiplash” dynamics).  \nThe repository provides modeling tools, numerical experiments, and theoretical notes for analyzing stability of systems subject to rapid changes in acceleration.\n\n---\n\n## Core Problem\n\nConsider a dynamical system\n\nx''(t) = F(x(t), x'(t), t)\n\nsubject to impulsive or rapidly varying forcing.\n\nThe stability objective is to determine conditions under which perturbations δx(t) remain bounded.\n\nLinearized perturbation equation\n\nδx'' = D_x F(x(t), x'(t), t) δx + D_{x'}F(x(t), x'(t), t) δx'\n\nA trajectory is stable if\n\nsup_t ||δx(t)|| \u003c ∞.\n\n---\n\n## Repository Structure\n\nsrc/  \ncore simulation and stability algorithms\n\nnotebooks/  \nnumerical experiments and demonstrations\n\ndocs/  \ntheoretical derivations and references\n\ntests/  \nvalidation of stability conditions\n\n---\n\n## Stability Methods\n\nThe repository explores several approaches:\n\n1. Lyapunov stability analysis\n2. Spectral analysis of linearized dynamics\n3. Energy methods for impulsive forcing\n4. Numerical integration under high-jerk conditions\n\n---\n\n## Example Model\n\nMass–spring–damper with impulsive forcing\n\nm x'' + c x' + k x = J(t)\n\nwhere J(t) represents short impulse forces.\n\nStability condition\n\nc \u003e 0  \nk \u003e 0\n\nEnergy\n\nE(t) = ½ m (x')² + ½ k x²\n\ndE/dt ≤ 0 ensures dissipative stability.\n\n---\n\n## Usage\n\nClone the repository\n\ngit clone https://github.com/inaciovasquez2020/whiplash-stability.git\n\nRun simulations\n\npython src/simulate.py\n\n---\n\n## Research Goals\n\n- Characterize stability under high-jerk motion\n- Provide numerical tools for analyzing impulsive dynamics\n- Develop energy-based stability bounds\n\n---\n\n## License\n\nMIT\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Finaciovasquez2020%2Fwhiplash-stability","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Finaciovasquez2020%2Fwhiplash-stability","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Finaciovasquez2020%2Fwhiplash-stability/lists"}