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An extended canonical perturbation method. (English) Zbl 0259.70013


MSC:

70H15 Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics
70K99 Nonlinear dynamics in mechanics

Software:

TRIGMAN
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Full Text: DOI

References:

[1] Bogoliubov, N. and Mitropolsky, Y.: 1961,Asymptotic Method in the Theory of Nonlinear Oscillations, Gordon and Breach, New York.
[2] Brouwer, D.: 1966, ?Solution of the Problem of Artificial Satellite Theory Without Drag,?Astron. J. 64, 378. · doi:10.1086/107958
[3] Brouwer, D. and Hori G.-I.: 1961, ?Theoretical Evaluation of Atmospheric Drag Effects in the Motion of an Artificial Satellite?,Astron. J. 66, 193. · doi:10.1086/108399
[4] Campbell, J. A. and Jefferys, W. H.: 1970, ?Equivalence of the Perturbation Theories of Hori and Deprit?,Celest. Mech. 2, 467. · Zbl 0205.55005 · doi:10.1007/BF01625278
[5] Deprit, A.: 1969, ?Canonical Transformations Depending on a Small Parameter?,Celest. Mech. 1, 12. · Zbl 0172.26002 · doi:10.1007/BF01230629
[6] Deprit, A. and Rom, A.: 1967, ?Asymptotic Representation of the Cycle of van der Pol’s Equation for Small Damping Coefficients,?Z. angew. Math. Physik,18, 736. · Zbl 0166.35202 · doi:10.1007/BF01602044
[7] Hildebrand, C. H., Jr.: 1969, ?A Discussion of Two General Perturbation Methods and Their Application to Artificial Satellite Theory?, TR-1004, Applied Mechanics Research Laboratory, The University of Texas at Austin, Austin, Texas.
[8] Hori, G-I.: 1966, ?Theory of General Perturbations with Unspecified Canonical Variables?,Astron. Soc. Japan,18, 4.
[9] Hori, G-I.: 1971, ?Theory of General Perturbation for Non-Canonical Systems?,Publ. Astron. Soc. Japan,23, 567.
[10] Jefferys, H.: 1970, ?TRIGMAN-A System for Algebraic Manipulations of Poisson Series?, Applied Mechanics Research Laboratory, Report No. AMRL 1032, The University of Texas at Austin, Austin, Texas (August 1970).
[11] Kamel, A.: 1970, ?Perturbation Method in the Theory of Nonlinear Oscillations?,Celest. Mech. 3, 90. · Zbl 0251.70013 · doi:10.1007/BF01230435
[12] Kamel, A. A.: 1971, ?Lie Transforms and the Hamiltonization of Non-Hamiltonian Systems?,Celest. Mech. 4, 397. · Zbl 0234.34069 · doi:10.1007/BF01231400
[13] Lane, M. H. and Crawford, K. H.: 1969, ?An Improved Analytical Drag Theory for the Artificial Satellite Problem?, AIAA/AAS Astrodynamics Conference, AIAA Paper 69-925.
[14] Mersman, W. A.: 1970a, ?A New Algorithm for the Lie Transformation?,Celest. Mech. 3, 81. · Zbl 0222.70021 · doi:10.1007/BF01230434
[15] Mersman, W. A.: 1970b, ?Explicit Recessive Algorithms for the Construction of Equivalent Canonical Transformations?,Celest. Mech. 3, 384. · Zbl 0228.70028 · doi:10.1007/BF01231807
[16] Powers, W. F. and McDonell, J. P.: 1970, ?Switching Conditions and a Synthesis Technique for the Singular Saturn Guidance Problem?, AIAA Guidance, Control and Flight Mechanics Conference, AIAA Paper No. 70-965, Santa Barbara, California, August, 1970.
[17] Powers, W. F. and Tapley, B. D.: 1969, ?Canonical Applications to Optimal Trajectory Analysis?,AIAA J. 7, 394. · Zbl 0175.21701 · doi:10.2514/3.5119
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.