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ACTION-ANGLE COORDINATES Adrian Price-Whelan
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n second order 2n first order
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n=3, 6D phase-space
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Integrable systems There exist n independent integrals of motion In 2n-dimensional phase-space:
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Integrable systems There exist n independent integrals of motion Motion is confined to an n-dimensional manifold In 2n-dimensional phase-space:
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Integrable systems Bounded motion periodicity
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Integrable systems What if…
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Integrable systems
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Action-angle coords.
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Action-angle coords.
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Action-angle coords.
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cool. SO WHAT?
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Tidal stream formation Hessian
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Tidal stream formation
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Position Velocity
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Angles Actions
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so how do we find actions?
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This is not a solved problem!
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Kaasalainen & Binney McGill & Binney Sanders & Binney Bovy