Wojciech Kalinowski
Pronouns: Mr
About
My research project
High Order Continuation Methods for Trajectory Design and Maintenance in Three Body ProblemIn recent years, there has been an increased interest in Lunar research, which motivates the exploration of its complex dynamic environment. Understanding the underlying dynamics, including the bifurcations of orbital trajectories, is essential for enabling more efficient transfers and station keeping in orbit. This PhD research proposes a novel semi-analytical approach based on Differential Algebra — a technique that leverages Taylor series expansions to operate on polynomial representations rather than on a single constant part numerical values. This method allows the evaluation of a small neighbourhood of points, to specified accuracy, to be calculated via simple polynomial evaluation.
The objectives of this PhD are to detect and classify various bifurcations of Periodic Orbits, to parameterise a complete Quasi-Periodic Tori, and to employ the parameterised tori as a reference for a new station-keeping strategy
Supervisors
In recent years, there has been an increased interest in Lunar research, which motivates the exploration of its complex dynamic environment. Understanding the underlying dynamics, including the bifurcations of orbital trajectories, is essential for enabling more efficient transfers and station keeping in orbit. This PhD research proposes a novel semi-analytical approach based on Differential Algebra — a technique that leverages Taylor series expansions to operate on polynomial representations rather than on a single constant part numerical values. This method allows the evaluation of a small neighbourhood of points, to specified accuracy, to be calculated via simple polynomial evaluation.
The objectives of this PhD are to detect and classify various bifurcations of Periodic Orbits, to parameterise a complete Quasi-Periodic Tori, and to employ the parameterised tori as a reference for a new station-keeping strategy
ResearchResearch interests
Astrodynamics, Orbital Mechanics, Bifurcation Theory, Dynamical System Theory, Continuation Methods
Research interests
Astrodynamics, Orbital Mechanics, Bifurcation Theory, Dynamical System Theory, Continuation Methods
Publications
Stability analysis of periodic orbits rely on linear analysis tools such as Floquet Multipliers or the Broucke stability diagram, typically aided by Monte Carlo simulations. However, these techniques fail to potentially capture the nonlinear behaviour of the system near bifurcations of linearly stable orbits. In this paper a novel approach is used to expand upon continuation methods to automatically gain insight into the nonlinear stability of periodic orbits and identify bifurcation via Differential Algebra and Lyapunov–Schmidt Reduction. Differential algebra enables representation of functions as Taylor polynomial series with mathematical operations defined on them enabling a locally dense semi-analytical solution. The Lyapunov–Schmidt method can give a bifurcation equation, coefficients of which can be compared to standard bifurcation equations to gain insight into higher order stability. The motivating example are the planar Quasi Satellite Orbits of the Mars Moon eXploer mission which exhibited linear stability but were nonlinearly unstable near the 1:3 subharmonic bifurcation. Results show that the Differential Algebra is capable of easily creating parametrised Poincare maps which can be used to get a bifurcation normal form via Lyapunov-Schmidt Method.