Identifying Time-Scale Structure for Simpli ed Guidance Law Development

Guidance law development for aerospace vehicles can be signi cantly simpli ed by reducing the order of the vehicle dynamic model. Identifying timescale separation in the system dynamics is important in this regard. This paper introduces a systematic means of identifying the time-scale structure in a nonlinear dynamical system by using regional Lyapunov exponents. Regional Lyapunov exponents and associated vectors are used to analyze the linear variational equations associated with a nonlinear system, in order to draw conclusions about the time-scale structure in the nonlinear system. Examples are used to illustrate the the time-scale information provided by the regional Lyapunov exponents. The time scale structure in an example of closed-loop entry dynamics is investigated using the regional Lyapunov exponents. The exponents and their associated directions identify energy as the slow variable and radial distance and ight path angle as fast variables and thus provide the information needed for reduced order guidance law development.