Computation of periodic solutions of conservative systems with application to the 3-body problem
We show how to compute families of periodic solutions of conservative systems with two-
point boundary value problem continuation software. The computations include detection of …
point boundary value problem continuation software. The computations include detection of …
Chebyshev–Taylor parameterization of stable/unstable manifolds for periodic orbits: implementation and applications
JD Mireles James, M Murray - International Journal of Bifurcation …, 2017 - World Scientific
This paper develops a Chebyshev–Taylor spectral method for studying stable/unstable
manifolds attached to periodic solutions of differential equations. The work exploits the …
manifolds attached to periodic solutions of differential equations. The work exploits the …
Continuation of quasi-periodic invariant tori
F Schilder, HM Osinga, W Vogt - SIAM Journal on Applied Dynamical Systems, 2005 - SIAM
Many systems in science and engineering can be modeled as coupled or forced nonlinear
oscillators, which may possess quasi-periodic or phase-locked invariant tori. Since there …
oscillators, which may possess quasi-periodic or phase-locked invariant tori. Since there …
VSVO formulation of the Taylor method for the numerical solution of ODEs
This paper presents an analysis of the Taylor method for the numerical solution of ODEs
when a very high precision of the solution is required. Some theoretical properties of the …
when a very high precision of the solution is required. Some theoretical properties of the …
Local orbital elements for the circular restricted three-body problem
The Keplerian orbital elements make up a set of parameters that uniquely describe a two-
body trajectory. Once perturbations are imposed on two-body dynamics, one often studies …
body trajectory. Once perturbations are imposed on two-body dynamics, one often studies …
Numerical computation of the normal behaviour of invariant curves of n-dimensional maps
À Jorba - Nonlinearity, 2001 - iopscience.iop.org
We describe a numerical method for computing the linearized normal behaviour of an
invariant curve of a diffeomorphism of Bbb R n, n⩾ 2. In the reducible case, the method …
invariant curve of a diffeomorphism of Bbb R n, n⩾ 2. In the reducible case, the method …
Dynamics around the Earth–Moon triangular points in the Hill restricted 4-body problem
This paper investigates the motion of a small particle moving near the triangular points of the
Earth–Moon system. The dynamics are modeled in the Hill restricted 4-body problem …
Earth–Moon system. The dynamics are modeled in the Hill restricted 4-body problem …
A parameterization method for the computation of invariant tori and their whiskers in quasi-periodic maps: explorations and mechanisms for the breakdown of …
In two previous papers [J. Differential Equations, 228 (2006), pp. 530-579; Discrete Contin.
Dyn. Syst. Ser. B, 6 (2006), pp. 1261-1300] we have developed fast algorithms for the …
Dyn. Syst. Ser. B, 6 (2006), pp. 1261-1300] we have developed fast algorithms for the …
[BOOK][B] Hamiltonian perturbation solutions for spacecraft orbit prediction: the method of Lie transforms
M Lara - 2021 - books.google.com
Analytical solutions to the orbital motion of celestial objects have been nowadays mostly
replaced by numerical solutions, but they are still irreplaceable whenever speed is to be …
replaced by numerical solutions, but they are still irreplaceable whenever speed is to be …
Two periodic models for the Earth-Moon system
This paper discusses two alternative models to the Restricted Three Body Problem (RTBP)
for the motion of a massless particle in the Earth-Moon system. These models are the …
for the motion of a massless particle in the Earth-Moon system. These models are the …