dynamic stabili zation of non-spherical bodies against unlimited collapse

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Dynamic stabilization of non-spherical bodies against unlimited collapse G.S. Bisnovatyi-Kogan 1,2,3 , O.Yu. Tsupko 1,3 1 Space Research Institute of Russian Academy of Science, Profsoyuznaya 84/32, Moscow 117997, Russia 2 Joint Institute Nuclear Research, Dubna, Russia 3 Moscow Engineering Physics Institute, Moscow, Russia e-mail: [email protected], [email protected]

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Dynamic stabili zation of non-spherical bodies against unlimited collapse. G . S. Bisnovatyi-Kogan 1,2,3 , O . Yu. Tsupko 1,3 1 Space Research Institute of Russian Academy of Science, Profsoyuznaya 84/32, Moscow 117997, Russia 2 Joint Institute Nuclear Research, Dubna, Russia - PowerPoint PPT Presentation

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Page 1: Dynamic stabili zation of non-spherical bodies against unlimited collapse

Dynamic stabilizationof non-spherical bodies

against 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, Russia3Moscow Engineering Physics Institute, Moscow, Russia

e-mail: [email protected], [email protected]

Page 2: Dynamic stabili zation of non-spherical bodies against unlimited collapse

Dynamic stability of spherical stars

Page 3: Dynamic stabili zation of non-spherical bodies against unlimited collapse

Non-rotating uniform 3-axis ellipsoid

Page 4: Dynamic stabili zation of non-spherical bodies against unlimited collapse
Page 5: Dynamic stabili zation of non-spherical bodies against unlimited collapse

Equations of motion

Page 6: Dynamic stabili zation of non-spherical bodies against unlimited collapse

Non-dimensional equations of motion

for spheroid

Page 7: Dynamic stabili zation of non-spherical bodies against unlimited collapse

Non-dimensional total energy(non-dimensional hamiltonian)

Page 8: Dynamic stabili zation of non-spherical bodies against unlimited collapse

Results of numerical calculations

Page 9: Dynamic stabili zation of non-spherical bodies against unlimited collapse
Page 10: Dynamic stabili zation of non-spherical bodies against unlimited collapse
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Page 12: Dynamic stabili zation of non-spherical bodies against unlimited collapse

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

Page 13: Dynamic stabili zation of non-spherical bodies against unlimited collapse
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Page 15: Dynamic stabili zation of non-spherical bodies against unlimited collapse

The chaotic motion

Page 16: Dynamic stabili zation of non-spherical bodies against unlimited collapse

The regular oscillations

Page 17: Dynamic stabili zation of non-spherical bodies against unlimited collapse

Discussion

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Page 19: Dynamic stabili zation of non-spherical bodies against unlimited collapse

• MNRAS, 2008, accepted

• Thank you for your attention