Abstract
The stability of the rolling motion of near space hypersonic vehicles with rudder control is studied using method of qualitative analysis of nonlinear differential equations, and the stability criteria of the deflected rolling motions are improved. The outcomes can serve as the basis for further study regarding the influence of pitching and lateral motion on the stability of rolling motion. To validate the theoretical results, numerical simulations were done for the rolling motion of two hypersonic vehicles with typical configurations. Also, wind tunnel experiments for four aircraft models with typical configurations have been done. The results show that: 1) there exist two dynamic patterns of the rolling motion under statically stable condition. The first one is point attractor, for which the motion of aircraft returns to the original state. The second is periodic attractor, for which the aircraft rolls periodically. 2) Under statically unstable condition, there exist three dynamic patterns of rolling motion, namely, the point attractor, periodic attractor around deflected state of rolling motion, and double periodic attractors or chaotic attractors.
Similar content being viewed by others
References
Rong Z. Study on the Flow Characteristic and Mechanism of Rolling Motions Induced by Fore-Body Vortex. Dissertation for Doctoral Degree. Beijing: Beijing University of Aeronautics and Astronautics, 2009
Xia X J, Liu R Z, Yang X F. Unsteady flow behavior of a slender delta wing rock. J Beijing Univ Aeron Astron, 1998, 24(2): 185–188
Huang D, Wu G X. Investigation on unsteady aerodynamic characteristics for a delta wing oscillating in large amplitude pitching roll motion. ACTA Aeron Astron Sin, 1999, 20(6): 485–488
Liu W. Nonlinear Analysis and Numerical Simulation of Rocks of Slender Wing. Dissertation for Doctoral Degree. Changsha: National University of Defense and Technology, 2004
Liu W, Zhang H X. Hopf bifurcation and numerical simulation of free rocks of wings. In: Proceedings of the First Symposium on Mechanic Problems of Aeronautics and Astronautics. Chengdu: Beijing University of Aeronautics and Astronautics, 2004. 110–115
Liu W, Zhang H X. Nonlinear analysis and numerical simulation of rocks of slender wing. In: the 12th Conference on Computational Fluid Dynamics. Xi’an: Chinese Aerodynamics Research Society, 2004. 361–367
Liu W, Zhang H X. Numerical simulation and physical characteristic analysis for slender wing rock. Chin J Theor Appl Mech, 2005, 37(4): 385–392
Zhang H X, Liu W, Xie Y F, et al. On the rocking motion and its dynamic evolution of a swept delta wing. Acta Aerodyn Sin, 2006, 24(1): 5–9
Liu W, Yang X L, Zhang H X, et al. A review of investigations of wing rock problems under high angle of attack. Adv Mech, 2008, 38(2): 214–228
Mehra R K, Kessel W C, Carroll J V. Global Stability and Control Analysis of Aircraft at High Angles of Attack. NASA, AD A051850, 1977
Hawkins C A. Application of Bifurcation and Catastrophe Theories to Near Stall Flight Mechanics. NASA, AD A 167697, 1985
Gao H, Zhu P S, Gao Z H. The Advance Flight Dynamics. Beijing: National Defense Industry Press, 2004
He Z D, Gao H. The Advance Flight Dynamics. Xi’an: Northwestern Polytechnical University Press, 1990
Liu C. Fundamental of Nonlinear Dynamic Characteristic Analysis of Aircraft. Nanjing: Press of Nanjing University of Aeronautics and Astronautics, 1982
Fang Z P, Chen W C, Zhang S G. Flight Dynamics of Aeronautic Vehicles. Beijing: Beihang Press, 2005
Zhang H X, Yuan X X, Ye Y D, et al. Research on the dynamic stability of an orbital reentry vehicle in pitching. ACTA Aerodyn Sin, 2002, 20(3): 247–259
Zhang H X, Zhang Z, Yuan X X, et al. Physical analysis and numerical simulation for the dynamic behavior of vehicles in pitching oscillations or rocking motions. Sci China Ser E-Technol Sci, 2007, 50(4): 385–401
He X M, Peng M S. Introduction of Partial Differential Equations and Dynamic Systems. Beijing: Beijing Institute of Technology Press, 2010
Zhang J Y, Feng B Y. Geometry Theory and Bifurcation of Partial Differential Equations. Beijing: Beijing University Press, 2000
Ma Z E, Zhou Y C. Qualitative and Stability Method of Partial Differential Equations. Beijing: Science Press, 2001
Zhang X F. Study on the Dynamic Characteristic of Hypersonic Vehicles. Dissertation for Doctoral Degree. Mianyang: China Aerodynamic Research and Development Center, 2012
Li H F. Guidance and Control Technique of Hypersonic Vehicles. Beijing: China Astronautic Publishing House, 2012
Li Y P, Zhao Z L, Li H. Experimental Tests on the Stability Criteria of One Freedom Rolling Motions. Technical Report, High Speed Institute of China Aerodynamic Research and Development Center, 2012
Li Y P, Zhao Z L. Experimental Tests on Dynamic Derivative of Body-Wing Configurations. Technical Report, High Speed Institute of China Aerodynamic Research and Development Center, 2012
Li Q C, Zhao Z L, Yang H Y, et al. Experimental Studies of Free Rolling Motions With Large Attack Angle in FL-24 Wind Tunnel. Technical Report, High Speed Institute of China Aerodynamic Research and Development Center, 2012
Author information
Authors and Affiliations
Corresponding author
Additional information
Recommended by ZHOU Heng (CAS Academician)
Rights and permissions
About this article
Cite this article
Ye, Y., Zhao, Z., Tian, H. et al. The stability analysis of rolling motion of hypersonic vehicles and its validations. Sci. China Phys. Mech. Astron. 57, 2194–2204 (2014). https://doi.org/10.1007/s11433-014-5603-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11433-014-5603-1