Analytical solution to 3D differential geometric guidance problem

The application of three-dimensional differential geometric (DG) guidance law is studied. Moreover, the Newton iterative algorithm is introduced to formulate an analytical solution of the differential geometric guidance system. First, the classical differential geometry theory is utilized to transform the guidance commands form an arc length system to the time domain. Then, an algorithm of angle of attack and side slide angle is developed to formulate the DG guidance system. Moreover, the Newton iterative algorithm is introduced to derive an analytical solution to the proposed guidance system. Simulation of intercepting non-maneuvering targets and maneuvering targets are performed, the results indicate that the proposed DG guidance law is a generalization of proportional navigation (PN) guidance. However, it performs better than traditional PN guidance in intercepting of maneuvering targets.