Loughborough University
Thesis-2020-Sheng.pdf (4.45 MB)

Stability and bifurcations in averaged models of dynamics

Download (4.45 MB)
posted on 2021-03-29, 08:41 authored by Mickey Sheng
Averaging over fast phases reduces study of stability of quasi-periodic and periodic trajectories to study of stability of periodic trajectories and equilibria. The aim of the proposed research is to study stability properties in several averaged models of dynamics. Bifurcation analysis is the central tool in study of such properties. The first and second models that we study are the simple and the spherical pendulums {with vibrating suspension points}. We give a complete description of bifurcations of their phase portraits. Main part of the research is devoted to the restricted elliptic three body problem (ER3BP). This model with large eccentricities of the planet is of particular interest in relation to study of motion of exoplanets.



  • Science


  • Mathematical Sciences


Loughborough University

Rights holder

© Kaicheng Sheng

Publication date



A thesis submitted in partial fulfilment of the requirements for the award of the degree of Doctor of Philosophy of Loughborough University.


  • en


Anatoly Neishtadt

Qualification name

  • PhD

Qualification level

  • Doctoral

This submission includes a signed certificate in addition to the thesis file(s)

  • I have submitted a signed certificate