10/junho/22 – Invariant Manifolds near L1 and L2 in the Planar Elliptic Restricted Three-Body Problem (Dr Gladston Duarte, AGH University of Science and Technology)

In this work we investigate the connections between the stable and unstable manifolds of tori around the points L1 and L2 of the Planar Elliptic Restricted Three-Body Problem (PERTBP).

The study of connections between the invariant manifolds of the periodic orbits around these points, in the Planar Circular RTBP, and the creation of bridges between different types of orbits was already done in [1].
In the case of considering an elliptical movement, we investigate how the analysis of the orbit of comet 39P/Oterma can be improved in a more quantitative way. We compute the dynamical objects that interact with this comet (mixing the tools presented in [2] and the parallel shooting technique), and use some temporal+spatial sections in the phase space to better visualize these objects together with Oterma, when fitting its data into this model.

References:
[1] Koon, W. S., Lo, M. W., Marsden, J. E., Ross, S. D.: ’Resonance and Capture of Jupiter Comets’, Celestial Mechanics and Dynamical Astronomy 81: 27-38, 2001.
[2] Jorba, À.: ’Numerical Computation of the Normal Behaviour of Invariant Curves of n-Dimensional Maps’, Nonlinearity 14: 943-976, 2001.