On the Application of the Competitive Modes Conjecture

Modelling natural phenomena via Dynamical System Theory has become commonplace amongst mathematicians, physicists, engineers, and the like. As such, research in this field is currently underway, with a notable focus on chaos. The Competitive Modes Conjecture is a relatively new approach in the field of chaotic Dynamical Systems, aiming to...

Low-energy transfers from GTO to lunar Halo orbits: rideshare options and sensitivities

In this research project, the design of a smallsat mission to a Halo orbit around the Earth-Moon second libration point (EML-2) using a rideshare launch opportunity to an inclined geosynchronous transfer orbit (GTO) was investigated. <br/>The design leverages classical results from Dynamical Systems Theory (DST) to determine low-energy transfers...

Connecting hyperbolic invariant manifolds at variations of the Poincaré section orientation: A numerical investigation into novel transfer solutions connecting collinear periodic libration point orbits through their associated manifold structures

The three-body problem (3BP) formulated by I. Newton has inspired many great mathematicians like L. Euler (1707-1783), J.L. Lagrange (1736-1813), K.G.J. Jacobi (1804-1851), W.R. Hamilton (1805-1865) and J.H. Poincaré (1854-1912) to develop mathematical studies, methods and theories in an attempt to solve this problem. Although these concepts...

Analysis of the Sun-Earth Lagrangian environment for the New Worlds Observer (NWO)

Exoplanets have been detected for more than 15 years. In the vast majority of instances, this has been accomplished through indirect observation. Such methods include among others the observation of radial velocity, transit photometry, and timing variations. These techniques allow for the vast majority of exoplanet detections up to date. An...

Interplanetary Trajectory Design using Dynamical Systems Theory

Instead of the two-body problem commonly used in interplanetary trajectory design, also three bodies can be considered: the satellite, a planet and the Sun. Knowing that planet and Sun orbit one another in almost circular orbits, and the mass of the satellite is negligible compared to the mass of these bodies, the model of the circular...

Weak capture and the weak stability boundary: An investigation into the restricted problem of three bodies

Weak capture in the restricted problem of three bodies refers to transitory motion between the primaries. Such behavior has interesting applications in space mission design, notably, in finding optimal transfer trajectories that surpass the performance of traditional Hohmann transfers. The Weak Stability Boundary (WSB) is a mathematical set that...