Relationship Between Impact Time Constrained Nonlinear Optimal Guidance and Euler Beam Deformation

This paper studies the relationship between the impact time constrained nonlinear optimal guidance (ITCNOG) problem and an Euler beam deformation problem. The ITCNOG problem is proved to be equivalent to an Euler beam deformation problem. The theory of elasticity could be adopted to obtain the optimal trajectory. This makes the ITCNOG problem easier to be solved, and avoids the non-convergence of numerical solvers. Numerical simulation verifies the effectiveness of the proposed optimal guidance law. In the same way, the impact time and angle constrained nonlinear optimal guidance (ITACNOG) problem could also be transformed to be an Euler beam deformation problem.