일시: 10/13(월) 13:00-14:00

제목: Symplectic geometry and astrodynamics - the story behind the research collaboration

초록: I am going to talk about how the collaboration started and how it has contributed to both mathematics and engineering communities enabling a better understanding of the effect of the dynamics under the influence of three bodies, especially the Jupiter-Europa system.

Studying astrodynamics is commonly approximated by classical mechanics and solved using differential calculus by engineers. The three-body problem is one of the key topics in astrodynamics, and it has been studied for decades. The brute-force differential equation solving approach has been predominantly used. However, engineers often confront several fundamental questions: are the two different solutions from the numerical computation qualitatively ‘different’? how are the solutions evolved? If there is a bifurcation, did the computation algorithm find all the bifurcation branches? If these questions can be answered, one solution can tell much about the dynamics of the orbit family, and engineers can confidently build the trajectory catalogue for any design requirement. Moreover, we will be able to understand dynamics around celestial bodies which is the primary goal of the study. Interestingly, there are close links between symplectic geometry and astrodynamics, sharing the same questions of the three-body problem. A few collaborators from the two fields including Agustin Moreno, Urs Frauenfelder, Cengiz Aydin, Otto van Koert,  and Dayung Koh have started an interdisciplinary study complementing each other's fields. As a result, the new symplectic geometry tools are successfully applied to trajectory searching in mission design and bifurcation study in the three-body problem.