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

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

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

Surrey Space Centre