Abstract
A noncanonical Hamiltonian formulation of the Coulomb formation dynamics is used to develop necessary conditions for static Coulomb formations with constant charges. With a static or frozen formation the satellites perform non-Keplerian orbits and maintain constant relative position vectors. As seen by an observer following the center of mass motion, the spacecraft formation would appear to behave equivalently to a rigid body in orbit. Previous research has demonstrated the existence of such static Coulomb formations analytically by employing symmetry simplifying assumptions with linearized relative motion dynamics, or by using numerical genetic search algorithms. These static solutions are used as reference geometries and charges for feedback law developments. This paper presents nonlinear static formation conditions for the circularly restricted problem. Hamiltonian formulations have been used to study equilibrium conditions of rigid bodies in orbit. Analogous techniques are employed to study necessary conditions to achieve a static Coulomb formation. Analytical results using the full and truncated formation gravity potential function are presented. Numerical results illustrate convergence performance improvements of an evolutionary search algorithm where the presented necessary conditions are enforced.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
BURNS, R., MCLAUGHLIN, C. A., LEITNER, J., et al. “TechSat 21: Formation Design, Control, and Simulation,” IEEE Aerospace Conference Proceedings, Big Sky, Montana, Vol. 7, March 18–25, 2000, pp. 19–25.
MIDDOUR, J.W. “Along Track Formationkeeping for Satellites With Low Eccentricity,” The Journal of the Astronautical Sciences, Vol. 41, No. 1, Jan.–March 1993, pp. 19–33.
TAPLEY, B.D., BETTADPUR, S., RIES, J. C., et al. “GRACE Measurements of Mass Variability in the Earth System,” Science, Vol. 305, No. 5683, 2004, pp. 503–505.
SWEETSER, T. H. “An End-to-End Trajectory Description of the LISA Mission,” Classical and Quantum Gravity, Vol. 22, No. 10, 2005, pp. 429–435.
KING, L. B., PARKER, G.G., DESHMUKH, S., et al. “Spacecraft Formation-Flying using Inter-Vehicle Coulomb Forces,” technical report, NASA/NIAC, January 2002, http://www.niac.usra.edu.
MULLEN, E.G., GUSSENHOVEN, M. S., and HARDY, D. A. “SCATHA Survey of High-Voltage Spacecraft Charging in Sunlight,” Journal of the Geophysical Sciences, Vol. 91, 1986, pp. 1074–1090.
TORKAR, K., et. al. “Active Spacecraft Potential Control for Cluster—Implementation and First Results,” Annales Geophysicae, Vol. 19, 2001, pp. 1289–1302.
KING, L. B., PARKER, G.G., DESHMUKH, S., and CHONG, J. “Study of Interspacecraft Coulomb Forces and Implications for Formation Flying,” AIAA Journal of Propulsion and Power, Vol. 19, No. 3, May–June 2003, pp. 497–505.
CHONG, J.-H., Dynamic Behavior of Spacecraft Formation Flying using Coulomb Forces, Masters thesis, Michigan Technological University, May 2002.
NATARAJAN, A. and SCHAUB, H. “Linear Dynamics and Stability Analysis of a Coulomb Tether Formation,” Journal of Guidance, Control, and Dynamics, Vol. 29, No. 4, July–Aug. 2006, pp. 831–839.
SCHAUB, H., PARKER, G.G., and KING, L. B. “Challenges and Prospect of Coulomb Formations,” The Journal of the Astronautical Sciences, Vol. 52, No. 1–2, Jan.–June 2004, pp. 169–193.
BERRYMAN, J. and SCHAUB, H. “Static Equilibrium Configurations in GEO Coulomb Spacecraft Formations,” presented as paper AAS 05-104 at the AAS Space Flight Mechanics Meeting, Copper Mountain, CO, Jan. 23–27, 2005.
JOE, H., SCHAUB, H., and PARKER, G.G. “Formation Dynamics of Coulomb Satellites,” presented at the 6th International Conference on Dynamics and Control of Systems and Structures in Space, Riomaggiore, Cinque Terre, Italy, July 2004.
SCHAUB, H. and JUNKINS, J. L. Analytical Mechanics of Space Systems, AIAA Education Series, Reston, VA, October 2003.
WANG, L.-S., MADDOCKS, J. H., and KRISHNAPRASAD, P. S. “Steady Rigid-Body Motions in a Central Gravitational Field,” The Journal of the Astronautical Sciences, Vol. 40, No. 4, 1992, pp. 449–478.
BECK, J. A. and HALL, C.D. “Relative Equilibria of a Rigid Satellite in a Circular Keplerian Orbit,” The Journal of the Astronautical Sciences, Vol. 46, No. 3, 1998, pp. 215–247.
NICHOLSON, D. R. Introduction to Plasma Theory, Krieger, 1992.
GOMBOSI, T. I. Physics of the Space Environment, Cambridge University Press, 1998.
CLOHESSY, W. H. and WILTSHIRE, R. S. “Terminal Guidance System for Satellite Rendezvous,” Journal of the Aerospace Sciences, Vol. 27, No. 9, Sept. 1960, pp. 653–658.
HILL, G.W. “Researches in the Lunar Theory,” American Journal of Mathematics, Vol. 1, No. 1, 1878, pp. 5–26.
BATTIN, R.H. An Introduction to the Mathematics and Methods of Astrodynamics, AIAA Education Series, New York, 1987.
BECK, J.A. Relative Equilibria of a Rigid Satellite in a Central Gravitational Field, Ph.D. dissertation, Air Force Institute of Technology, Wright-Patterson AFB, OH, Sept. 1997, AFIT/DS/ENY/97-6.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Schaub, H., Hall, C.D. & Berryman, J. Necessary conditions for circularly-restricted static coulomb formations. J of Astronaut Sci 54, 525–541 (2006). https://doi.org/10.1007/BF03256504
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF03256504