Solving relative two-point boundary value problems: Spacecraft formation flight transfers application

Journal of Guidance, Control, and Dynamics

Volumn 27, Issue 4, 2004, Pages 693-704

  Guibout, V M ^a,b   Scheeres, D J ^a,b  

^a UNIVERSITY OF MICHIGAN   (United States)

^b Aerospace Engineering Department   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; DEGREES OF FREEDOM (MECHANICS); EARTH (PLANET); EQUATIONS OF MOTION; FLIGHT DYNAMICS; HAMILTONIANS; MATHEMATICAL TRANSFORMATIONS; PROBLEM SOLVING; SPACECRAFT;

CANONICAL TRANSFORMATIONS; HAMILTON-JACOBI EQUATION; LEGENDRE TRANSFORMATIONS; SPATIAL DOMAINS;

BOUNDARY VALUE PROBLEMS;

EID: 3843132880     PISSN: 07315090     EISSN: 15333884     Source Type: Journal    
DOI: 10.2514/1.11164     Document Type: Article

References (18)

1. Zhan, H., Xu, B., and Zhang, Z. M., "An Analytical Approach to Analyzing Spacecraft Formation-Flying Motion," AIAA Paper 2002-4847, Aug. 2002.
2. Richardson, D. L., and Mitchell, J. W., "A Third-Order Analytical Solution for Relative Motion with a Circular Reference Orbit," AAS/AIAA Space Flight Mechanics Meeting, Vol. 112, Pt. 1, American Astronautical Society, Springfield, VA, 2002, pp. 605-615.
3. Alfriend, K. T., Yan, H., and Valadi, S. R., "Nonlinear Considerations in Satellite Formation Flying," AIAA Paper 2002-4741, Aug. 2002.
4. Wang, P. K. C., and Hadaegh, F. Y., "Minimum-Fuel Formation Reconfiguration of Multiple Free-Flying Spacecraft," Journal of the Astronautical Sciences, Vol. 47, Nos. 1-2, 1999, pp. 77-102.
5. Goldstein, H., Classical Mechanics, Addison Wesley Longman, Reading, MA, 1965.
6. Greenwood, D. T., Classical Dynamics, Prentice-Hall, Upper Saddle River, NJ, 1977.
7. Channell, P. J., and Scovel, J. C., "Symplectic Integration of Hamiltonian Systems," Nonlinearity, Vol. 3, No. 2, 1990, pp. 231-259.
8. Abraham, R., and Marsden, J. E., Foundations of Mechanics, 2nd ed., W. A. Benjamin, Reading, MA, 1978.
9. Arnold, V. I., Mathematical Methods of Classical Mechanics, 2nd ed., Springer-Verlag, Berlin, 1988, p. 267.
10. Guibout, V. M., and Scheeres, D. J., "Formation Flight with Generating Functions: Solving the Relative Boundary Value Problem," AIAA Paper 2002-4639, Aug. 2002.
11. Lanczos, C., The Variational Principles of Mechanics, 4th ed., Univ. of Toronto Press, Toronto, 1977.
12. Marsden, J. E., and Ratiu, T. S., Introduction to Mechanics and Symmetry: A Basic Exposition of Classical Mechanical Systems, 2nd ed., Springer-Verlag, Berlin, 1998.
13. Battin, R. H., An Introduction to the Mathematics and Methods of Astrodynamics, rev. ed., AIAA, Reston, VA, 1999.
14. Arnold, V. I., Catastrophe Theory, 3rd rev. and expanded ed., Springer-Verlag, Berlin, 1992.
15. Ehlers, J., and Newman, E. T., "The Theory of Caustics and Wavefront Singularities with Physical Applications," Journal of Mathematical Physics A, Vol. 41, No. 6, 2000, pp. 3344-3378.
16. Hörmander, L., Seminar on Singularities of Solutions of Linear Partial Direrential Equations, Princeton Univ. Press, Princeton, NJ, 1979.
17. Arnold, V. I., Kozlov, V. V., and Neishtadt, A. I., Mathematical Aspects of Classical and Celestial Mechanics, Dynamical Systems III, Springer-Verlag, Berlin, 1988.
18. Scheeres, D. J., Han, D., and Hou, Y., "Influence of Unstable Manifolds on Orbit Uncertainty," Journal of Guidance, Control, and Dynamics, Vol. 24, No. 3, 2004, pp. 573-585.