Logarithmic Navigation for Precise Guidance of Space Vehicles

The principles of logarithmic guidance are derived and their application to various space-flight guidance problems is discussed. Logarithmic guidance is shown to be ideal during the terminus of control where considerations of minimum fuel, minimum heating etc., can be subordinated to precise matching of vehicle kinematics to the desired trajectory. This precise trajectory control is achieved utilizing velocity and position measurements to govern the vehicle deceleration. Multidimensional effects are considered and it is shown that various "degrees of control" of velocity vector magnitude and angle, time of arrival, accelerations, geographical or inertial directions of approach, etc., can be achieved. The tolerance of logarithmic guidance to instrumentation errors and parameter variations are confirmed by error analyses of these guidance principles applied to the control of the velocity vector during the deceleration process.