Separatrix crossing in rotation of a body with changing geometry of masses

Jinrong Bao, Anatoly Neishtadt

Research output: Contribution to journalArticlepeer-review


We consider free rotation of a body whose parts move slowly with respect to each other under the action of internal forces. This problem can be considered as a perturbation of the Euler-Poinsot problem. The dynamics has an approximate conservation law-an adiabatic invariant. This allows us to describe the evolution of rotation in the adiabatic approximation. The evolution leads to an overturn in the rotation of the body: the vector of angular velocity crosses the separatrix of the Euler-Poinsot problem. This crossing leads to a quasirandom scattering in body's dynamics. We obtain formulas for probabilities of capture into different domains in the phase space at separatrix crossings.

Original languageEnglish
Pages (from-to)150-171
Number of pages22
JournalSIAM Journal on Applied Dynamical Systems
Issue number1
Publication statusPublished - 2019
Externally publishedYes


  • Adiabatic invariant
  • Rigid body dynamics
  • Separatrix crossing

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