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Dynamic Stability of Non-Spherical Bodies: Finite Versus Chaotic Behavior

Explore dynamic stabilization of non-spherical bodies against unlimited collapse through numerical calculations and analysis of chaotic versus regular oscillations. Discuss results in the context of non-rotating uniform 3-axis ellipsoids.

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Dynamic Stability of Non-Spherical Bodies: Finite Versus Chaotic Behavior

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  1. Dynamic stabilizationof non-spherical bodiesagainst unlimited collapse G.S. Bisnovatyi-Kogan1,2,3 , O.Yu. Tsupko1,3 1Space Research Institute of Russian Academy of Science, Profsoyuznaya 84/32, Moscow 117997, Russia 2Joint Institute Nuclear Research, Dubna, Russia 3Moscow Engineering Physics Institute, Moscow, Russia e-mail: gkogan@iki.rssi.ru, tsupko@iki.rssi.ru

  2. Dynamic stability of spherical stars

  3. Non-rotating uniform 3-axis ellipsoid

  4. Equations of motion

  5. Non-dimensional equations of motion for spheroid

  6. Non-dimensional total energy(non-dimensional hamiltonian)

  7. Results of numerical calculations

  8. The regular oscillations are represented by closed lines on the Poincar´e map, and chaotic behavior fills regions of finite square with dots.

  9. The chaotic motion

  10. The regular oscillations

  11. Discussion

  12. MNRAS, 2008, accepted • Thank you for your attention

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