Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 2 of 2
Full-Text Articles in Physical Sciences and Mathematics
Existence Of A Periodic Brake Orbit In The Fully Symmetricplanar Four Body Problem, Ammon Si-Yuen Lam
Existence Of A Periodic Brake Orbit In The Fully Symmetricplanar Four Body Problem, Ammon Si-Yuen Lam
Theses and Dissertations
We investigate the existence of a symmetric singular periodic brake orbit in the equal mass, fully symmetric planar four body problem. Using regularized coordinates, we remove the singularity of binary collision for each symmetric pair. We use topological and symmetry tools in our investigation.
Four-Body Problem With Collision Singularity, Duokui Yan
Four-Body Problem With Collision Singularity, Duokui Yan
Theses and Dissertations
In this dissertation, regularization of simultaneous binary collision, existence of a Schubart-like periodic orbit, existence of a planar symmetric periodic orbit with multiple simultaneous binary collisions, and their linear stabilities are studied. The detailed background of those problems is introduced in chapter 1. The singularities of simultaneous binary collision in the collinear four-body problem is regularized in chapter 2. We use canonical transformations to collectively analytically continue the singularities of the simultaneous binary collision solutions in both the decoupled case and the coupled case. All the solutions are found and more importantly, we find a crucial first integral which describes …