High-order continuation methods for trajectory design and maintenance in restricted three-body problems

A fully funded PhD opportunity to join the Space Trajectory Analysis Group of the Surrey Space Centre and pioneer innovative trajectory design techniques for calculating periodic and quasi-periodic orbits in chaotic astrodynamics problems.

Start date

1 April 2024


3.5 years

Application deadline

Funding source

US Air Force Office for Scientific Research

Funding information

  • UKRI standard stipend
  • Budget for 1x European conference and 1x international conference (e.g. International Astronautical Congress / AAS/AIAA Space Flight Mechanics Meeting, AAS/AIAA Astrodynamics Specialist Conference).


The application of numerical continuation techniques to the study of non-integrable astrodynamics problems has paved the way to innovative space trajectory designs and substantial propellant savings. However, traditional predictor corrector techniques remain exposed to branch switching, a phenomenon known in the literature of dynamical systems theory to cause the omission of important dynamical features such as changes in stability and bifurcations. We propose to upgrade numerical continuation techniques by means of the differential algebra of Taylor polynomials, thereby gaining access to high-order derivatives that can aid mission designers in detecting bifurcations, recognizing nonlinear stability regions, and more robustly operating spacecraft in chaotic dynamical environments. The PhD researcher will be trained in differential algebra and high-order continuation techniques to gain insight into the dynamical evolution of spacecraft in the cislunar environment [1]. Such a dynamical model is gaining in popularity thanks to the uprising of the ARTEMIS programme and the desire of returning human beings back to the surface of the Moon since the end of the Apollo era.

[1] https://openresearch.surrey.ac.uk/esploro/outputs/99537223702346

Eligibility criteria

Open to candidates who pay UK/home rate fees. See UKCISA for further information. The international applicants are welcome to apply, as long as they can cover or self-fund the difference between home and overseas tuition fees. You will need to meet the minimum entry requirements for our PhD programme.

Essential skills:

  • Code programming (MATLAB, C/C++, and/or similar)

Desired skills:

  • Strong Mathematical Background
  • Knowledge of Restricted Three-Body problems 
  • Knowledge of Dynamical Systems Theory
  • Independent thinking

How to apply

Applications should be submitted via the Space Engineering PhD programme page. In place of a research proposal you should upload a document stating the title of the project that you wish to apply for and the name of the relevant supervisor.

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Application deadline

Contact details

Nicola Baresi
30 BA 01
Telephone: +44 (0)1483 688272
E-mail: n.baresi@surrey.ac.uk

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