Discover how exponential screening alters classical orbits, breaking symmetry to drive precessing rosettes and unstable potential cliff collapse.

https://youtu.be/8ZVbjQvG9e4

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🍃Precessing Rosettes and Spiral Collapse Mechanics in Screened Gravitational Fields

Discover how exponential screening in attractive Yukawa fields breaks elliptical symmetry, driving non-closing precessing rosette orbits and rapid dissipative spiral capture into central targets.

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🍄Deliverables 21

Precession and Orbital Collapse in Screened Potentials

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Documents

• Computational and numerical models (Yukawa.md)
• Snippets
• Conceptual physics and energy landscapes (The Physics of Screening.md)

Exploration Frontiers

• Bound Rosette Orbits $\rightarrow$ Analytic Perturbation Theory
• Unstable Potential Cliff $\rightarrow$ Analytical Critical Momentum
• Dissipative Spiral Capture $\rightarrow$ Quantum Wave-Packet Tunneling
• Repulsive Short-Range Scattering $\rightarrow$ Core-Repulsive Generalized Potentials

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}}%%
graph LR
    subgraph Current_Exploration["Current Exploration (R21: Non-Inverse-Square Dynamics)"]
        A(Bound Rosette Orbits):::current
        B(Unstable Potential Cliff):::current
        C(Dissipative Spiral Capture):::current
        D(Repulsive Short-Range Scattering):::current
    end

    subgraph Potential_Orientation["Potential Orientation (Extensions & Formalisms)"]
        E(Analytic Perturbation Theory: Δϕ):::potential
        F(Analytical Critical Momentum: Lc):::potential
        G(Quantum Wave-Packet Tunneling):::potential
        H(Core-Repulsive Generalized Potentials):::potential
    end

    %% Theoretical Mappings
    A -- "Derive closed-form formula for periastron shift" --> E
    B -- "Solve dVeff/dr=0 for bifurcation boundary" --> F
    C -- "Transition from dissipation to quantum TDSE" --> G
    D -- "Extend to models with r⁻¹² repulsive cores" --> H

    %% Styling Definitions
    classDef current fill:#0277bd,stroke:#01579b,color:#ffffff,stroke-width:2px;
    classDef potential fill:#2e7d32,stroke:#1b5e20,color:#ffffff,stroke-width:2px;
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    style Potential_Orientation fill:#e8f5e9,stroke:#a5d6a7,stroke-width:2px,color:#1b5e20;

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