Login | Register

Periodic Orbits Associated with the Libration Points of the Homogeneous Rotating Gravitating Triaxial Ellipsoid

Title:

Periodic Orbits Associated with the Libration Points of the Homogeneous Rotating Gravitating Triaxial Ellipsoid

Romanov, Volodymyr A. and Doedel, Eusebius (2012) Periodic Orbits Associated with the Libration Points of the Homogeneous Rotating Gravitating Triaxial Ellipsoid. International Journal of Bifurcation and Chaos, 22 (10). p. 1230035. ISSN 0218-1274

[img]
Preview
Text (application/pdf)
doedel2012a.pdf - Accepted Version
2MB

Official URL: http://dx.doi.org/10.1142/S0218127412300352

Abstract

We present computational results for the families of periodic orbits that emanate from the five libration points of the homogeneous gravitating triaxial ellipsoid rotating around its small axis, as well as for various secondary bifurcating families. Possible applications of our results include research on the motion of stars and clusters in elliptical galaxies, and the design of space missions to the vicinity of small bodies (asteroids) and their libration points. The numerical continuation and bifurcation algorithms employed in our study are based on boundary value techniques, as implemented in the AUTO software tool.

Divisions:Concordia University > Gina Cody School of Engineering and Computer Science > Computer Science and Software Engineering
Item Type:Article
Refereed:Yes
Authors:Romanov, Volodymyr A. and Doedel, Eusebius
Journal or Publication:International Journal of Bifurcation and Chaos
Date:October 2012
Digital Object Identifier (DOI):10.1142/S0218127412300352
Keywords:Celestial mechanics; bifurcation analysis; periodic orbits; rotating gravitating ellipsoid; missions to asteroids; libration points; numerical continuation
ID Code:977332
Deposited By: DANIELLE DENNIE
Deposited On:11 Jun 2013 19:18
Last Modified:18 Jan 2018 17:44

References:

V. K. Abalkin , Proc. Instit. Theoret. Astron. 8, 8 (1957).
J. Bak and T. S. Statler , The Astron. J. 120, 110 (2000), DOI: 10.1086/301437
Yu. V. Batrakov , Proc. Instit. Theoret. Astron. 8, 524 (1957).
G. Bertin , Dynamics of Galaxies ( Cambridge University Press , 2000 ) .
D. T. Britt , Asteroids III, eds. W. F. Bottke Jr. (University of Arizona Press, Tucson, 2002) pp. 485–500.
N. D. Caramicolas and H. Varvoglis , Astron. Astrophys. 141, 383 (1984).
N. D. Caramicolas , Astron. Astrophys. 282, 34 (1994).
A. Celletti , Stability and Chaos in Celestial Mechanics ( Praxis Publishing , Chichester, UK , 2010 ) .
A. Cellino , Astron. Astrophys. 219, 320 (1989).
Collins, G. W. II [1978] The Virial Theorem in Stellar Astrophysics, available via ads.harvard.edu/books/1978vtsa.book/ .
R. L. Davies , Encyclopedia of Astronomy & Astrophysics, ed. P. Murdin (IOP Publishing Ltd., 2006) pp. 1–8.
E. Davoust , Astron. Astrophys. 125, 101 (1983).
E. Davoust , Astron. Astrophys. 156, 152 (1986).
D. J. Dichmann , E. J. Doedel and R. C. Paffenroth , Libration Point Orbits and Applications, eds. G. Goméz , M. W. Lo and J. J. Masdemont (World Scientific, Singapore, 2003) pp. 429–488.
E. J. Doedel , Int. J. Bifurcation and Chaos 13, 1 (2003).
E. J. Doedel , Int. J. Bifurcation and Chaos 17, 2625 (2007).
G. N. Duboshin , Celestial Mechanics. The Principal Problems and Methods ( Nauka , Moscow , 1968 ) .
A. Elipe and M. Lara , The J. Astronaut. Sci. 51, 391 (2003).
J. Galán , Phys. Rev. Lett. 88, 4 (2002).
S. A. Gasanov and L. G. Lukyanov , Astron. Rep. 46, 851 (2002), DOI: 10.1134/1.1515096
G. Gómez , Dynamics and Mission Design Near Libration Points, Vol. I: Fundamentals, The Case of Collinear Libration Points ( World Scientific , Singapore , 2001 ) .
G. Gómez , Dynamics and Mission Design Near Libration Points, Vol. II: Fundamentals, The Case of Triangular Libration Points ( World Scientific , Singapore , 2001 ) .
D. R. Gregory , Classical Mechanics ( Cambridge University Press , 2006 ) .
W. Hu and D. J. Scheeres , J. Guid. Contr. Dyn. 25, 765 (2002), DOI: 10.2514/2.4944
C. Hunter , Ann. NY Acad. Sci. 867, 61 (1998), DOI: 10.1111/j.1749-6632.1998.tb11250.x
M. A. Jalali , B. Mehri and S. H. Pourtakdoust , Celest. Mech. Dyn. Astron. 63, 271 (1996), DOI: 10.1007/BF00692291
W. G. Koon , Dynamical Systems, the Three-Body Problem and Space Mission Design ( 2006 ) .
B. Krauskopf , H. M. Osinga and J. Galán-Vioque (eds.) , Numerical Continuation Methods for Dynamical Systems — Path Following and Boundary Value Problems , Springer Series on 'Understanding Complex Systems' ( Springer-Verlag , 2007 ) .
L. G. Lukyanov and S. A. Gasanov , Astron. Astrophys. Trans. 22, 529 (2003), DOI: 10.1080/1055679031000086531
A. P. Markeyev , The Libration Points in Celestial Mechanics and Space Dynamics ( Nauka , Moscow , 1978 ) .
D. Merrit , Dynamics of triaxial stellar systems, The Nature of Elliptical Galaxies, Proc. 2nd Stromlo Symp., eds. M. Arnaboldi , G. S. Da Costa and P. Saha (1996) p. 11.
K. Meyer , G. Hall and D. Offin , Introduction to Hamiltonian Dynamical Systems and the N-Body Problem, Applied Mathematical Sciences 90 (2009) pp. 271–299.
F. E. Muñoz-Almaraz , Celest. Mech. Dyn. Astron.: An Int. J. Space Dyn. 97, 17 (2007).
H. Poincaré , Les Méthodes Nouvelles de la Mécanique Céleste , History of Modern Physics and Astronomy ( Springer , 1892 ) .
Project Galileo [2006] Asteroid Gaspra; Asteroid Ida and Dactil, available via www2.jpl.nasa.gov/galileo/slides/slide10.html and www2.jpl.nasa.gov/galileo/slides/slide18.html .
Y. Revaz and D. Pfenniger , Astron. Astrophys. 372, 784 (2001), DOI: 10.1051/0004-6361:20010571
F. P. J. von Rimrott , Introductory Orbit Dynamics ( Braunschweig , Wiesbaden, Vieweg , 1989 ) .
Romanov, V. A. [2005] "Elemental periodic solutions of the circular restricted 3-body problem," M. Comp. Sci Thesis (Dept. of Computer Science, Concordia University, Montreal) .
D. J. Scheeres , Icarus 110, 225 (1994), DOI: 10.1006/icar.1994.1118 [ CrossRef ] .
D. J. Scheeres , Icarus 121, 67 (1996), DOI: 10.1006/icar.1996.0072 [ CrossRef ] .
D. J. Scheeres , B. G. Williams and J. K. Miller , J. Guid. Contr. Dyn. 23, 466 (2000), DOI: 10.2514/2.4552
L. S. Sparke and J. S. Gallagher , Galaxies in the Universe: An Introduction ( Cambridge University Press , 2000 ) .
P. C. Thomas , Science 277, 1492 (1997), DOI: 10.1126/science.277.5331.1492
P. C. Thomas , Icarus 128, 88 (1997), DOI: 10.1006/icar.1997.5736
B. Viateau and M. Rappoport , Astron. Astrophys. 370, 602 (2001), DOI: 10.1051/0004-6361:20010222 .
C. von Kirchbach , Trajectoriesleaving a sphere in the restricted 3-body problem, 15th AAS/AIAA Spaceflight Mechanics Meeting (Copper Mountain, CO, 2005) p. 27.
W. E. Wisel , Spacecraft Dynamics ( McGraw-Hill Book Company , 1989 ) .
S. G. Zhuravlev , Celest. Mech. 6, 255 (1972).
S. G. Zhuravlev , Celest. Mech. 8, 75 (1973).
M. T. Zuber , Science 289, 1788 (2000), DOI: 10.1126/science.289.5487.2097
All items in Spectrum are protected by copyright, with all rights reserved. The use of items is governed by Spectrum's terms of access.

Repository Staff Only: item control page

Downloads per month over past year

Back to top Back to top