Polynomial expansions of single-mode motions around equilibrium points in the circular restricted three-body problem

Polynomial expansions of single-mode motions around equilibrium points in the circular restricted... In this work, the single-mode motions around the collinear and triangular libration points in the circular restricted three-body problem are studied. To describe these motions, we adopt an invariant manifold approach, which states that a suitable pair of independent variables are taken as modal coordinates and the remaining state variables are expressed as polynomial series of them. Based on the invariant manifold approach, the general procedure on constructing polynomial expansions up to a certain order is outlined. Taking the Earth–Moon system as the example dynamical model, we construct the polynomial expansions up to the tenth order for the single-mode motions around collinear libration points, and up to order eight and six for the planar and vertical-periodic motions around triangular libration point, respectively. The application of the polynomial expansions constructed lies in that they can be used to determine the initial states for the single-mode motions around equilibrium points. To check the validity, the accuracy of initial states determined by the polynomial expansions is evaluated. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Celestial Mechanics and Dynamical Astronomy Springer Journals

Polynomial expansions of single-mode motions around equilibrium points in the circular restricted three-body problem

34 pages
Read Article

Loading next page...
 
/lp/springer_journal/polynomial-expansions-of-single-mode-motions-around-equilibrium-points-LwsHdwa0Vk
Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer Science+Business Media B.V., part of Springer Nature
Subject
Physics; Astrophysics and Astroparticles; Dynamical Systems and Ergodic Theory; Aerospace Technology and Astronautics; Geophysics/Geodesy; Classical Mechanics
ISSN
0923-2958
eISSN
1572-9478
DOI
10.1007/s10569-018-9828-6
Publisher site
See Article on Publisher Site

Abstract

In this work, the single-mode motions around the collinear and triangular libration points in the circular restricted three-body problem are studied. To describe these motions, we adopt an invariant manifold approach, which states that a suitable pair of independent variables are taken as modal coordinates and the remaining state variables are expressed as polynomial series of them. Based on the invariant manifold approach, the general procedure on constructing polynomial expansions up to a certain order is outlined. Taking the Earth–Moon system as the example dynamical model, we construct the polynomial expansions up to the tenth order for the single-mode motions around collinear libration points, and up to order eight and six for the planar and vertical-periodic motions around triangular libration point, respectively. The application of the polynomial expansions constructed lies in that they can be used to determine the initial states for the single-mode motions around equilibrium points. To check the validity, the accuracy of initial states determined by the polynomial expansions is evaluated.

Journal

Celestial Mechanics and Dynamical Astronomy – Springer Journals

Published: May 8, 2018

References

  • Leaving the Moon by means of invariant manifolds of libration point orbits
    Alessi, EM; Gómez, G; Masdemont, JJ
  • Two-maneuvres transfers between LEOs and Lissajous orbits in the Earth–Moon system
    Alessi, EM; Gómez, G; Masdemont, JJ
  • The Halo family of three dimensional periodic orbits in the Earth–Moon restricted three body problem
    Breakwell, JV; Brown, J
  • Non-linear normal modes, invariance, and modal dynamics approximations of non-linear systems
    Boivin, N; Pierre, C; Shaw, SW
  • Computing natural transfers between Sun–Earth and Earth–Moon Lissajous libration point orbits
    Canalias, E; Masdemont, JJ
  • The parameterization method for invariant manifolds III: overview and applications
    Cabré, X; Fontich, E; De, L
  • Quantitative Analysis Method for Strongly Nonlinear Vibration System
    Chen, SH
  • Low energy transit orbits in the restricted three-body problem
    Conley, CC
  • Properties of transit trajectory in the restricted three and four-body problem
    Circi, C
  • Natural families of periodic orbits
    Deprit, A; Henrard, J
  • Elemental periodic orbits associated with the libration points in the circular restricted 3-body problem
    Doedel, EJ; Romanov, VA; Paffenroth, RC
  • Future missions for libration-point satellites
    Farquhar, RW
  • On the high order approximation of the centre manifold for ODEs
    Farrés, A; Jorba, À
  • Applications of multi-body dynamical environments: the ARTEMIS transfer trajectory design
    Folta, DC; Woodard, M; Howell, K
  • High-order analytical solutions of Hill’s equations
    Gómez, G; Marcote, M
  • Numerical exploration of the restricted problem V, Hill case: periodic orbits and their stability
    Hénon, M
  • The Parameterization Method for Invariant Manifolds
    Haro, À; Luque, A; Mondelo, JM
  • On motions around the collinear libration points in the elliptic restricted three-body problem
    Hou, XY; Liu, L
  • On quasi-periodic motions around the collinear libration points in the real Earth–Moon system
    Hou, XY; Liu, L
  • Dynamics in the center manifold of the collinear points of the restricted three body problem
    Jorba, À; Masdemont, J
  • Dynamical Systems, the Three-Body Problem and Space Mission Design
    Koon, WS; Lo, MW; Marsden, JE; Ross, SD
  • High-order analytical solutions around triangular libration points in circular restricted three-body problem
    Lei, HL; Xu, B
  • High-order solutions of invariant manifolds associated with libration point orbits in the elliptic restricted three-body system
    Lei, HL; Xu, B; Hou, XY; Sun, YS
  • High-order solutions around triangular libration points in the elliptic restricted three-body problem and applications to low energy transfers
    Lei, HL; Xu, B
  • Analytical study on the motions around equilibrium points of restricted four-body problem
    Lei, HL; Xu, B
  • Transfers between libration point orbits of Sun-Earth and Earth–Moon systems by using invariant manifolds
    Lei, HL; Xu, B
  • Invariant manifolds around artificial equilibrium points for low-thrust propulsion spacecraft
    Lei, HL; Xu, B
  • High-order expansions of invariant manifolds of libration point orbits with application to mission design
    Masdemont, JJ
  • Nonlinear modal analysis of structural systems using multi-mode invariant manifolds
    Pesheck, E; Boivin, N; Pierre, C; Shaw, SW
  • Analytical and numerical construction of vertical periodic orbits about triangular libration points based on polynomial expansion relations among directions
    Qian, YJ; Yang, XD; Zhai, GQ
  • Analytic construction of periodic orbits about the collinear points
    Richardson, DL
  • Normal modes for non-linear vibratory systems
    Shaw, SW; Pierre, C
  • An invariant manifold approach to nonlinear normal modes of oscillation
    Shaw, SW
  • Normal modes of vibration for non-linear continuous systems
    Shaw, SW; Pierre, C
  • Theory of Orbits
    Szebehely, V
  • Results of the MUSES-A “HITEN” mission
    Uesugi, K
  • A new constellation configuration scheme for communicating architecture in cislunar space
    Xu, M; Wang, J; Liu, S
  • Three-dimensional periodic orbits about the triangular equilibrium points of the restricted problem of three bodies
    Zagouras, CG

You’re reading a free preview. Subscribe to read the entire article.

Try 2 weeks free now

DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

or browse the journals available

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create folders to
organize your research

Export folders, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off

Sign up
for free
Start 14 day
Free Trial