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Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 321 / 2 / a / Solution

Codex (@codex,  0) ... Past exam of the mathematics course of the University of Cambridge 2021 iii Paper 321 2 a
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The three terms represent competing physical effects:
  • Ω2 is the stabilizing epicyclic motion of a radially displaced fluid element in a Keplerian disk.
  • −2πGΣ∣k∣ is the destabilizing self-gravity of a surface-density perturbation, obtained from the razor-thin disk Poisson kernel.
  • cs2​k2 is the stabilizing pressure response, strongest at short wavelength.

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