Capiński, Maciej
Loading...
Email Address
Employee
aktywny
Alternative name
Discipline
matematyka
Author Profiles
Systemy AGH
2 results
Search Results
Now showing 1 - 2 of 2
Item type:Article, Access status: Open Access , Breakdown of homoclinic orbits to L3: Nonvanishing of the Stokes constant(2025) Baldomá, Inmaculada; Capiński, Maciej; Giralt, Mar; Guardia, Marcel
Wydział Matematyki StosowanejThe Restricted Planar Circular 3-Body Problem models the mo- tion of a body of negligible mass under the gravitational influence of two mas- sive bodies, called the primaries, which perform circular orbits coplanar with that of the massless body. In rotating coordinates, it can be modelled by a two degrees of freedom Hamiltonian system, which has five critical points called the Lagrange points. Among them, the point L3 is a saddle-center which is collinear with the primaries and beyond the largest of the two. The papers [3, 4] provide an asymptotic formula for the distance between the one dimensional stable and unstable manifolds of L3 in a transverse section for small values of the mass ratio 0 < μ ≪ 1. This distance is exponentially small with respect to μ and its first order depends on what is usually called a Stokes constant. The non-vanishing of this constant implies that the distance between the invariant manifolds at the section is not zero. In this paper, we prove that the Stokes constant is non-zero. The proof is computer assisted.Item type:Article, Access status: Open Access , Computer assisted proofs for transverse collision and near collision orbits in the restricted three body problem(2023) Capiński, Maciej; Keplay, Shane; Mireles-James, Jason
Wydział Matematyki StosowanejThis paper considers two point boundary value problems for conservative systems defined in multiple coordinate systems, and develops a flexible a posteriori framework for computer assisted existence proofs. Our framework is applied to the study collision and near collision orbits in the circular restricted three body problem. In this case the coordinate systems are the standard rotating coordinates, and the two Levi-Civita coordinate systems regularizing collisions with each of the massive primaries. The proposed framework is used to prove the existence of a number of orbits which have long been studied numerically in the celestial mechanics literature, but for which there are no existing analytical proofs at the mass and energy values considered here. These include transverse ejection/collisions from one primary body to the other, Strömgren’s asymptotic periodic orbits (transverse homoclinics for $L_{4,5}$), families of periodic orbits passing through collision, and orbits connecting $L_{4}$ to ejection or collision.