Analysis of non-dimensional forms of singular perturbation structures for hypersonic vehicles

In guidance and control of many aerospace vehicles, based on the knowledge of the speed of the state variables or the dynamics and previous experience in working with particular problems, a singularly perturbed structure is assumed by artificial insertion of a small unit-valued parameter with highest derivative or some of the state variables of the nonlinear dynamical equations. However, attempts have been made to identify the singular perturbation structure in terms of the parameters of the nonlinear dynamical system leading to a natural occurrence of the small parameter responsible for the singular perturbation structure. In this paper, further investigations are explored in identifying the singular perturbation parameter by using non-dimensional forms for the nonlinear dynamical equations. In particular, four different structures of identifying the singular perturbation parameter are presented and the various features of these structures are discussed.