Equations of Motion of a Hinged Body Over a Spherical Earth.

摘要

The six-degree-of-freedom (6-DOF) equations of motion are derived in vector form for a hinged vehicle flying over a spherical Earth. Initially, the most general form of the equations is developed assuming that the combustor may roll with respect to the body, as well as deflect in pitch and yaw. Next, the primary case is developed in which the combustor cannot roll with respect to the body. Finally, these equations are specialized to dime simpler cases. The motivation for deriving this set of equations is to support feasibility studies of the low drag ramjet (LDR), which is streamlined by deleting all aerodynamic surfaces. AH directional control comes from thrust vectoring, which is accomplished by deflecting the entire motor rather than just the exhaust nozzle, as in more conventional designs. Since the motor is a large fraction of the total vehicle mass, its inertia has a significant effect on the dynamics of the overall vehicle. Sufficient detail is included to serve as a tutorial.... Equations of motion.