Litcius/Paper detail

Applications of knot theory to the detection of heteroclinic connections between quasi-periodic orbits

D. B. Owen, Nicola Baresi

2024Astrodynamics11 citationsDOIOpen Access PDF

Abstract

Abstract Heteroclinic connections represent unique opportunities for spacecraft to transfer between isoenergetic libration point orbits for zero deterministic Δ V expenditure. However, methods of detecting them can be limited, typically relying on human-in-the-loop or computationally intensive processes. In this paper we present a rapid and fully systematic method of detecting heteroclinic connections between quasi-periodic invariant tori by exploiting topological invariants found in knot theory. The approach is applied to the Earth–Moon, Sun–Earth, and Jupiter–Ganymede circular restricted three-body problems to demonstrate the robustness of this method in detecting heteroclinic connections between various quasi-periodic orbit families in restricted astrodynamical problems.

Topics & Concepts

Heteroclinic cycleTorusPeriodic orbitsHeteroclinic orbitInvariant (physics)Knot theoryKnot (papermaking)MathematicsHeteroclinic bifurcationTopology (electrical circuits)Pure mathematicsPhysicsComputer scienceMathematical analysisGeometryHomoclinic orbitCombinatoricsMathematical physicsEngineeringHopf bifurcationNonlinear systemBifurcationChemical engineeringQuantum mechanicsAstro and Planetary ScienceStellar, planetary, and galactic studiesSpacecraft Dynamics and Control