Hostname: page-component-848d4c4894-nmvwc Total loading time: 0 Render date: 2024-06-26T13:14:17.355Z Has data issue: false hasContentIssue false

Algebraic analysis of stability and bifurcation for nonlinear flight dynamics

Published online by Cambridge University Press:  27 January 2016

D. Wang*
Affiliation:
Laboratoire d’Informatique de Paris 6, Université Pierre et Marie Curie – CNRS, Paris, France

Abstract

This note presents an application of algebraic methods to derive exact conditions for certain nonlinear flight dynamical systems to exhibit stability and bifurcation. The roll-coupling flight model is taken as an example to show the feasibility of algebraic analysis. Some of the previous stability and bifurcation results obtained using numerical analysis for this model are confirmed.

Type
Research Article
Copyright
Copyright © Royal Aeronautical Society 2011 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Buchberger, B. Gröbner bases: an algorithmic method in polynomial ideal theory, Multidimensional Systems Theory, Reidel, Dordrecht, 1985, pp 184232.Google Scholar
2. Collins, G.E. and Hong, H. Partial cylindrical algebraic decomposition for quantifier elimination, J Symbolic Computation, 1991, 12, (3), pp 299328.Google Scholar
3. El Kahoui, M. and Weber, A. Deciding Hopf bifurcations by quantifier elimination in a software-component architecture, J Symbolic Computation, 2000, 30, (2), pp 161179.Google Scholar
4. Goman, M.G. and Khramtsovsky, A.V. Global stability analysis of nonlinear aircraft dynamics, AIAA paper 97-3721, AIAA Guidance, Navigation, and Control Conference and Exhibit, New Orleans, US, 1997, pp 662672.Google Scholar
5. Goman, M.G. and Khramtsovsky, A.V. Computational framework for investigation of aircraft nonlinear dynamics, Advances in Engineering Software, 2008, 39, (3), pp 167177.Google Scholar
6. Goman, M.G., Zagainov, G.I. and Khramtsovsky, A.V. Application of bifurcation methods to nonlinear flight dynamics problems, Progress in Aerospace Sciences, 1997, 33, (9), pp 539586.Google Scholar
7. Kuznetsov, Y.A. Elements of Applied Bifurcation Theory, 2nd ed, Springer, New York, US, 1998.Google Scholar
8. Lazard, D. and Rouillier, F. Solving parametric polynomial systems, J Symbolic Computation, 2007, 42, (6), pp 636667.Google Scholar
9. Miller, R.K. and Michel, A.N. Ordinary Differential Equations, Academic Press, New York/London, UK, 1982.Google Scholar
10. Niu, W. and Wang, D. Algebraic approaches to stability analysis of biological systems, Mathematics in Computer Science, 2008, 1, (3), pp 507539.Google Scholar
11. Schy, A.A. and Hannah, M.E. Prediction of jump phenomena in rollcoupled manoeuvre of airplanes, J Aircr, 1977, 14, (4), pp 375382.Google Scholar
12. Sinha, N.K. and Ananthkrishnan, N. Maximum steady roll rate in zero-sideslip roll manoeuvers of aircraft, J Aircr, 2002, 39, (5), pp 897899.Google Scholar
13. Wang, D. Elimination Methods, Springer, Wien/New York, US, 2001.Google Scholar
14. Wang, D. Elimination Practice: Software Tools and Applications, Imperial College Press, London, UK, 2004.Google Scholar
15. Wang, D. and Xia, B. Stability analysis of biological systems with real solution classication, Proceedings of the 2005 International Symposium on Symbolic and Algebraic Computation, ACM Press, New York, US, 2005, pp 354361.Google Scholar
16. Wu, W.-T. Mathematics Mechanization, Science Press and Kluwer Academic, Beijing, China, 2000.Google Scholar
17. Yang, L. and Xia, B. Real solution classications of parametric semi-algebraic systems, Algorithmic Algebra and Logic – Proceedings of the A3L 2005, Herstellung und Verlag, Norderstedt, 2005, pp 281289.Google Scholar
18. Young, J.W., Schy, A.A. and Jonson, K.G. Pseudo-steady-state analysis of nonlinear aircraft manoeuvers, NASA technical paper 1758, December 1980.Google Scholar