Eigenvalue perturbation analysis of thrust law effects on hypersonic flight dynamics

A novel approach is proposed using the eigenvalue perturbation theory to analyze the thrust law effects of advanced air-breathing engines on hypersonic longitudinal dynamics. It is noticed that the influences of thrust laws are determined not only by the thrust characteristics, but also by the sensitivity of flight dynamics. By appropriate linear decomposition of the system matrix, the contributions of these two factors are analyzed using the eigenvalue perturbation theory. The influences of thrust laws are examined by their contributions to the 2-norm of the perturbation matrix. The sensitivities of the longitudinal modes of motion are examined according to their eigenvalue condition numbers. It is concluded that the phugoid mode is much more sensitive to thrust laws than the short period mode, and the thrust/speed dependence is the dominant factor that influences the flight stability. A detailed development of the method along with its application to a benchmark hypersonic vehicle Winged-cone as an example is included.