American Institute of Mathematical Sciences

Advanced
2005, 2005(Special): 297-306. doi: 10.3934/proc.2005.2005.297

Spacecraft dynamics near a binary asteroid

F. Gabern 1, , W.S. Koon 1, and  Jerrold E. Marsden 2,

1. 

Control and Dynamical Systems, California Institute of Technology, 107-81, 1200 E. California Boulevard, Pasadena, CA 91125, United States, United States
2. 

Control and Dynamical Systems 107-81, California Institute of Technology, Pasadena, CA 91125, United States

Received  September 2004 Revised  May 2005 Published  September 2005

We study a simple model for an asteroid pair, namely a planar system consisting of a rigid body and a sphere. This model is interesting because it is one of the simplest that captures the coupling between rotational and translational dynamics. By assuming that the binary is in a relative equilibria of the system, we construct a model for the motion of a spacecraft about this asteroid pair without affecting its motion (that is, we consider a restricted problem). This model can be studied as a perturbation of the standard Restricted Three Body Problem (RTBP). We use the stable zones near the triangular relative equilibrium points of the binary and a normal form of the Hamiltonian to compute stable periodic and quasi-periodic orbits for the spacecraft, which enable it to observe the binary while the binary orbits around the Sun.
Keywords: normal forms, spacecraft dynamics., Binary asteroids.
Mathematics Subject Classification: 37N05,70F0.
Citation: F. Gabern, W.S. Koon, Jerrold E. Marsden. Spacecraft dynamics near a binary asteroid. Conference Publications, 2005, 2005 (Special) : 297-306. doi: 10.3934/proc.2005.2005.297
[1]

Luigi Chierchia, Gabriella Pinzari. Planetary Birkhoff normal forms. Journal of Modern Dynamics, 2011, 5 (4) : 623-664. doi: 10.3934/jmd.2011.5.623
[2]

Shui-Nee Chow, Kening Lu, Yun-Qiu Shen. Normal forms for quasiperiodic evolutionary equations. Discrete & Continuous Dynamical Systems - A, 1996, 2 (1) : 65-94. doi: 10.3934/dcds.1996.2.65
[3]

Xingwu Chen, Weinian Zhang. Normal forms of planar switching systems. Discrete & Continuous Dynamical Systems - A, 2016, 36 (12) : 6715-6736. doi: 10.3934/dcds.2016092
[4]

A. Katok and R. J. Spatzier. Nonstationary normal forms and rigidity of group actions. Electronic Research Announcements, 1996, 2: 124-133.

[5]

Marco Abate, Francesca Tovena. Formal normal forms for holomorphic maps tangent to the identity. Conference Publications, 2005, 2005 (Special) : 1-10. doi: 10.3934/proc.2005.2005.1
[6]

Boris Kalinin, Victoria Sadovskaya. Normal forms for non-uniform contractions. Journal of Modern Dynamics, 2017, 11: 341-368. doi: 10.3934/jmd.2017014
[7]

P. De Maesschalck. Gevrey normal forms for nilpotent contact points of order two. Discrete & Continuous Dynamical Systems - A, 2014, 34 (2) : 677-688. doi: 10.3934/dcds.2014.34.677
[8]

Weigu Li, Jaume Llibre, Hao Wu. Polynomial and linearized normal forms for almost periodic differential systems. Discrete & Continuous Dynamical Systems - A, 2016, 36 (1) : 345-360. doi: 10.3934/dcds.2016.36.345
[9]

Ricardo Miranda Martins. Formal equivalence between normal forms of reversible and hamiltonian dynamical systems. Communications on Pure & Applied Analysis, 2014, 13 (2) : 703-713. doi: 10.3934/cpaa.2014.13.703
[10]

Vincent Naudot, Jiazhong Yang. Finite smooth normal forms and integrability of local families of vector fields. Discrete & Continuous Dynamical Systems - S, 2010, 3 (4) : 667-682. doi: 10.3934/dcdss.2010.3.667
[11]

Tomas Johnson, Warwick Tucker. Automated computation of robust normal forms of planar analytic vector fields. Discrete & Continuous Dynamical Systems - B, 2009, 12 (4) : 769-782. doi: 10.3934/dcdsb.2009.12.769
[12]

Majid Gazor, Mojtaba Moazeni. Parametric normal forms for Bogdanov--Takens singularity; the generalized saddle-node case. Discrete & Continuous Dynamical Systems - A, 2015, 35 (1) : 205-224. doi: 10.3934/dcds.2015.35.205
[13]

Alessandro Fortunati, Stephen Wiggins. Normal forms à la Moser for aperiodically time-dependent Hamiltonians in the vicinity of a hyperbolic equilibrium. Discrete & Continuous Dynamical Systems - S, 2016, 9 (4) : 1109-1118. doi: 10.3934/dcdss.2016044
[14]

Teresa Faria. Normal forms for semilinear functional differential equations in Banach spaces and applications. Part II. Discrete & Continuous Dynamical Systems - A, 2001, 7 (1) : 155-176. doi: 10.3934/dcds.2001.7.155
[15]

Andreas Henrici. Symmetries of the periodic Toda lattice, with an application to normal forms and perturbations of the lattice with Dirichlet boundary conditions. Discrete & Continuous Dynamical Systems - A, 2015, 35 (7) : 2949-2977. doi: 10.3934/dcds.2015.35.2949
[16]

Tsonka Baicheva. All binary linear codes of lengths up to 18 or redundancy up to 10 are normal. Advances in Mathematics of Communications, 2011, 5 (4) : 681-686. doi: 10.3934/amc.2011.5.681
[17]

John Burke, Edgar Knobloch. Normal form for spatial dynamics in the Swift-Hohenberg equation. Conference Publications, 2007, 2007 (Special) : 170-180. doi: 10.3934/proc.2007.2007.170
[18]

Amer Rasheed, Aziz Belmiloudi, Fabrice Mahé. Dynamics of dendrite growth in a binary alloy with magnetic field effect. Conference Publications, 2011, 2011 (Special) : 1224-1233. doi: 10.3934/proc.2011.2011.1224
[19]

Chun-Hao Teng, I-Liang Chern, Ming-Chih Lai. Simulating binary fluid-surfactant dynamics by a phase field model. Discrete & Continuous Dynamical Systems - B, 2012, 17 (4) : 1289-1307. doi: 10.3934/dcdsb.2012.17.1289
[20]

Tian Ma, Shouhong Wang. Cahn-Hilliard equations and phase transition dynamics for binary systems. Discrete & Continuous Dynamical Systems - B, 2009, 11 (3) : 741-784. doi: 10.3934/dcdsb.2009.11.741

 Impact Factor: 

Tools

Metrics

  • PDF downloads (6)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences