University of Surrey

Test tubes in the lab Research in the ATI Dance Research

On collision trajectories in the three body problem.

Hagen, Luke J. (2016) On collision trajectories in the three body problem. Doctoral thesis, University of Surrey.

thesisFinal.pdf - Version of Record
Available under License Creative Commons Attribution Non-commercial Share Alike.

Download (27MB) | Preview


In recent decades, the complex dynamics of the three body problem have been harnessed to accomplish missions that could be achieved in no other way with current technology; however, its potential has not been leveraged for missions that end in collision with one of the bodies. This research focuses on the opportunities that the three body dynamics around the secondary provide to missions that end in collision. Previous research in the Surrey Space Centre introduced a tool called the motion map which was an initial condition map that showed the discrete end state of each trajectory. Various con gurations of motion maps allowed for the identi cation of low ∆V temporary capture about the secondary or the planning of trajectories between regions of the three body problem. The aims of this research are to explore the structure of three body collision trajectories and provide mission designers with novel trajectory options that end in collision with the secondary. In this research, a critical structure was identified between bound and collision regions in motion maps and was found to be persistent across a range of energies and three body systems throughout the solar system. Motion maps were rst generalised amongst systems, showing their features are qualitatively the same. The collision trajectory structure was explored using a new tool created for this research called the collision map, which re ects certain parameters of the impact state onto the initial condition grid. Collision maps revealed that the characteristics of sets of collision trajectories are grouped in bubbles defined by constant numbers of periapsis passages prior to impact. Location within the bubble determines features such as impact angle, impact latitude and longitude, and impact velocity, while the location of the bubble on the collision map determines initial eccentricity and inclination, and an approximate time to a possible collision with the secondary. In order to explain the structure observed in collision maps, a perturbation model was derived. This model was applied to each trajectory on the motion map and explains many features of the motion map that were previously unknown. A method to re ne the model’s constants of motion which describe the average motion of a trajectory in the circular restricted three body problem (CR3BP) was developed and implemented. Trajectory design implications and considerations are addressed through a combination of collision maps and analytical curves that allow the search space for advantageous collision trajectories within the CR3BP to be reduced.

Item Type: Thesis (Doctoral)
Subjects : circular restricted three body problem, collision trajectories
Divisions : Theses
Authors :
Hagen, Luke
Date : 31 October 2016
Funders : Surrey Space Centre, United States Air Force
Contributors :
ContributionNameEmailORCID, P.L.
Depositing User : Luke Hagen
Date Deposited : 03 Nov 2016 09:26
Last Modified : 31 Oct 2017 18:45

Actions (login required)

View Item View Item


Downloads per month over past year

Information about this web site

© The University of Surrey, Guildford, Surrey, GU2 7XH, United Kingdom.
+44 (0)1483 300800