Multiple time-scales in nonlinear flight mechanics: Diagnosis and modeling

Applied Mathematics and Computation

Volumn 164, Issue 2, 2005, Pages 627-648

  Mease, K D ^a  

^a Irvine   (United States)

Author keywords

Nonlinear systems; Singular perturbations; Time scales

Indexed keywords

AIRCRAFT; COMPUTER SIMULATION; DEGREES OF FREEDOM (MECHANICS); EIGENVALUES AND EIGENFUNCTIONS; FLIGHT DYNAMICS; KINETIC ENERGY; MATHEMATICAL MODELS; PERTURBATION TECHNIQUES; POTENTIAL ENERGY;

NONLINEAR DYNAMICAL SYSTEMS; SINGULAR PERTURBATION; TIME-SCALES; TRANSLATIONAL DYNAMICS;

NONLINEAR SYSTEMS;

EID: 15544366004     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2004.06.015     Document Type: Conference Paper

References (27)

1. D.S. Naidu, and A.J. Calise Singular perturbations and time scales in guidance and control of aerospace systems: a survey J. Guidance Contr. 24 6 2001 1057 1078
2. A.E. Bryson Jr., M.N. Desai, and W.C. Hoffman Energy-state approximation in performance optimization of supersonic aircraft J. Aircraft 6 6 1969 481 488
3. H.J. Kelley Aircraft maneuver optimization by reduced-order approximations C.T. Leondes Control and Dynamic Systems 1973 Academic Press New York 131 178
4. H.J. Kelley, E.M. Cliff, and A.R. Weston Energy state revisited Opt. Contr. Appl. Meth. 7 1986 175 200
5. M.D. Ardema Solution of the minimum time-to-climb problem by matched asymptotic expansions AIAA J. 7 1976 845 850
6. P.V. Kokotovic, H.K. Khalil, and J. O'Reilly Singular Perturbation Methods in Control: Analysis and Design 1986 Academic Press New York
7. M.D. Ardema, and N. Rajan Separation of time scales in aircraft trajectory optimization J. Guidance Contr. 8 2 1985 275 278
8. A.J. Calise, N. Markopoulos, and J.E. Corban Nondimensional forms for singular perturbation analyses of aircraft energy climbs J. Guidance Contr. 17 3 1994 584 590
9. N. Fenichel Geometric singular perturbation theory for ordinary differential equations J. Diff. Eqs. 31 1979 53 98
10. C.K.R.T. Jones Geometric singular perturbation theory L. Arnold Dynamical Systems, Montecatini Terme Lecture Notes in Mathematics vol. 1609 1994 Springer-Verlag Berlin 44 118
11. T.J. Kaper An introduction to geometric methods and dynamical systems theory for singular perturbation problems Proc. Symp. Appl. Math. 56 1999 85 131
12. U. Maas, and S.B. Pope Simplifying chemical kinetics: intrinsic low-dimensional manifolds in composition space Combust. Flame 88 1992 239 264
13. T. Kaper, and H. Kaper Asymptotic analysis of two reduction methods for chemical kinetics Physica D 165 2002 66 93
14. S.H. Lam Using CSP to understand complex chemical kinetics Combust. Sci. Technol. 89 5-6 1993 375 404
15. S.H. Lam, and D.A. Goussis The CSP method of simplifying kinetics Int. J. Chem. Kinet. 26 1994 461 486
16. T. Kaper, A. Zagaris, and H. Kaper Analysis of the computational singular perturbation reduction method for chemical kinetics J. Nonlinear Sci. 14 2004 59 91
17. M.R. Roussel, and S.J. Fraser Geometry of the steady-state approximation: perturbation and accelerated convergence methods J. Chem. Phys. 93 3 1990 1072 1081
18. A.M. Lyapunov The general problem of stability of motion Int. J. Contr. 55 3 1992 531 773
19. L. Barreira, and Y.B. Pesin Lyapunov Exponents and Smooth Ergodic Theory University Lecture Series vol. 23 2002 American Mathematical Society Providence
20. K.D. Mease Geometry of computational singular perturbations A.J. Krener D.Q. Mayne Nonlinear Control System Design vol. 2 1996 Pergamon Oxford, UK 855 861
21. K.D. Mease, S. Bharadwaj, and S. Iravanchy Timescale analysis for nonlinear dynamical systems J. Guidance, Contr. Dynam. 26 2 2003 318 330
22. E.N. Lorenz The local structure of a chaotic attractor in 4-dimensions Physica D 13 1984 90 104
23. A. Trevisan, and R. Legnani Transient error growth and local predictability: a study in the Lorenz system Tellus 47A 1995 103 117
24. M. Spivak A Comprehensive Introduction to Differential Geometry, second ed. vol. 1 1979 Publish or Perish, Inc. Berkeley
25. A. Rao, and K.D. Mease Dichotomic basis approach to solving hypersensitive optimal control problems Automatica 35 1999 633 642
26. L. Dieci, R.D. Russell, and E.S. Van Vleck On the computation of Lyapunov exponents for continuous dynamical systems SIAM J. Num. Anal. 34 1 1997 402 423
27. I. Goldhirsch, P.-L. Sulem, and S.A. Orszag Stability and Lyapunov stability of dynamical systems: a differential approach and a numerical method Physica D 27 1987 311 337