PhD projects in Dynamics of Spacecraft, Satellites and Underwater
Below are some examples of PhD projects in dynamics of spacecraft, satellites and underwater vehicles. Alternative projects might be formulated following discussions with individual staff members, just contact the staff member or PhD admissions tutor Dr Gianne Derks.
Theory and numerics of reversing symmetry breaking bifurcations of Hamiltonian relative periodic orbits (Supervisor: Dr Claudia Wulff)
Relative periodic orbits (RPOs) of symmetric dynamical systems are
periodic orbits for the symmetry reduced system. Both the theory and
numerics of periodic orbits of general dynamical systems is
well-developed. But additional structure such as time-reversing and
preserving symmetries and symplecticity changes the generic behaviour
of dynamical systems dramatically. Recently there has been a lot of
progress in the development of a bifurcation theory for symmetric and
Hamiltonian systems, but the theory is far from being complete. In
particular the bifurcation theory of reversible symmetric periodic and
relative periodic orbits, is still in its beginning, as is the numerical
analysis of symmmetry breaking bifurcations of reversible periodic
orbits. The topic of this project is to analyze reversing symmetry breaking
bifurcations of RPOs theoretically and to derive and implement
numerical methods for their detection and computation within the
package SYMPERCON of Wulff, Schebesch, Schilder.
The results will be applied to various symmetric Hamiltonian
systems, in particular to N-body systems.
