Abstract
This paper focuses on the phugoid dynamic characteristic of hypersonic gliding vehicle. By regarding equilibrium glide as the fixed state of reentry trajectory, the dynamic equations are simplified and a hyper-geometric equation with a forcing function is deduced. Linearization theory is applied to analyze the characteristic of the motion, and the phugoid mode is found to be stable. An analytical solution of flight path angle as a function of speed is derived based on General Multiple Scale theory. The dynamic characteristic is analyzed, and the analytic solution is found to be in good agreement with the numerical simulation. When the initial states do not satisfy equilibrium glide condition or perturbation occurs, a damped oscillation along the equilibrium glide trajectory would occur. The damping diminishes as the speed decreases. The number of oscillations is decided by the lift-to-drag ratio, the initial altitude and the initial/final speed.
Similar content being viewed by others
References
Timothy R J, Cobb R G. Three-dimensional trajectory optimization satisfying waypoint and no-fly zone constraints. J Guid Control Dyn, 2009. 32: 551–572
DARPA. FALCON force application and launch from CONUS. BAA 03-35. 2004
Hueter U, Hutt J J. NASA’s next generation launch technology program-next generation space access roadmap. AIAA 2003-6941. 2003
Bollino K P. High-fidelity real-time trajectory optimization for reusable launch vehicles. Dissertation for the Doctoral Degree. California: Naval Postgraduate School. 2006
Richie G. The common aero vehicle: space delivery system of the future. AIAA 99-4435. 1999
Etkin B. Longitudinal dynamics of a lifting vehicle in orbital flight. J Aerosp Sci, 1961, 28: 779–788
Rangi R S. Non-linear effects in the longitudinal dynamics of a lifting vehicle in orbital flight. UTIA TN-40, 1960
Laitone E V, Chou Y S. Phugoid oscillations at hypersonic speeds. AIAA J, 1965, 3: 732–737
Vinh N X. Longitudinal dynamics stability of a shuttle vehicle. AIAA 70-977. 1970
Vinh N X. Hypersonic and planetary entry flight mechanics. Ann Arbor: the University of Michigan Press, 1980
Vinh N X, Chern J S, Lin C F. Phugoid oscillations in optimal reentry trajectorie. Acta Astronaut, 1981, 8: 311–324
Berry D T. National aerospace plane longitudinal long-period dynamics. J Guid Control Dyn, 1991, 14: 205–206
Sachs G. Effect of thrust/speed dependence on long-period dynamics in supersonic flight. J Guid Control Dyn, 1990, 13: 1163–1166
Sachs G. Thrust/speed effects on long-term dynamics of aerospace planes. J Guid Control Dyn, 1992, 15: 1050–1053
Ferreira L de O. Nonlinear dynamics and stability of hypersonic reentry vehicles. Dissertation for the Doctoral Degree. Michigan: University of Michigan, 1995
Snell S A. Nonlinear dynamic-inversion flight control of supermaneuverable aircraft. Twin Cities: University of Minnesota, 1991
Ramnath R V, Sandri G. A Generalized multiple scales approach to a class of linear differential equation. J Math Anal Appl, 1969, 28: 229–364
Ramnath R V, Sinha P. Dynamics of the space shuttle during entry into earth’s atmosphere. AIAA J, 1975, 113
Tao Y. Satellite attitude prediction by multiple time scales method. Massachusetts Institute of Technology. Dissertation for the Doctoral Degree. 1976
Radovsky S E. Sensitivity analysis of slowly-varying systems as applied to a VTOL airplane. Dissertation for the Master Degree. Cambridge: Massachusetts Institute of Technology, 1978
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Chen, X., Hou, Z., Liu, J. et al. Phugoid dynamic characteristic of hypersonic gliding vehicles. Sci. China Inf. Sci. 54, 542–550 (2011). https://doi.org/10.1007/s11432-011-4196-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11432-011-4196-9