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SUMMARY:Adiabatic approximation in studies of mean motion resonances in ce
 lestial mechanics - Prof. Vladislav Sidorenko (Keldysh Institute\, Moscow)
DTSTART:20200309T140000Z
DTEND:20200309T150000Z
UID:TALK136474@talks.cam.ac.uk
CONTACT:Chris Hamilton
DESCRIPTION:In the last decades of the XXth century\, it became clear that
  when studying resonant effects in dynamics of celestial bodies\, it is us
 eful to pay attention to the behavior of approximate integrals of motion c
 alled adiabatic invariants (Henrard and Lemaitre 1983\; Wisdom 1985). The 
 standard scheme of the adiabatic approximation in the investigations of me
 an motion resonances (MMR) as a first step involves averaging over the fas
 test dynamic process\, i.e. over the orbital motion of the objects in comm
 ensurability. In averaged equations of motion one should take a subsystem 
 that describes the process of “intermediate” time scale - the variatio
 n of the resonant angle. This subsystem can be interpreted as a Hamiltonia
 n system with one degree of freedom\, depending on other variables as slow
 ly varying parameters. Consequently\, the value of the “action” variab
 le for this subsystem will be an adiabatic invariant (AI). Studying then t
 he properties of level surfaces of AI in the subspace of the slowest varia
 bles\, we can draw conclusions about the secular evolution of the orbits o
 f celestial bodies in MMR. More delicate situation arises in the case of n
 onuniqueness of the resonant modes allowed by the system (Sidorenko et al.
  2014\; Sidorenko 2018). In particular\, in this case it is necessary to i
 dentify regions in the phase space\, where resonant modes can coexist\, to
  compare the probabilities of the capture into different modes\, and to an
 alyze the possibility of a transition between these modes. Fortunately\, t
 he theory of AI allows to do almost all of this. All phenomena under the d
 iscussion are illustrated by examples of their possible implementation in 
 the dynamics of real celestial bodies.
LOCATION:MR14\,  Centre for Mathematical Sciences\, Wilberforce Road\, Cam
 bridge
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