Linear guidance laws for space missions

High-order state transition polynomial with time expansion based on differential algebra

“…For the problem with variable propagation time, a linearized state and time transition matrix method is available in the literature [17][18][19]. Starting from the conventional STM, an additional term is added to include time perturbations and compute the associated time partial derivative [17], so that the corresponding STM terms for a time perturbation can be obtained.…”

“…Starting from the conventional STM, an additional term is added to include time perturbations and compute the associated time partial derivative [17], so that the corresponding STM terms for a time perturbation can be obtained. This turns out to be useful in linear guidance or covariance analysis with multiple event triggers [18,19]. Since orbital states usually show nonlinearity on time deviation, a novel high-order method is here introduced to propagate state variation throughout a relatively longer time duration.…”