In simulations of the flight of an inertially guided rocket vehicle, it is customary to represent the translational motion of the vehicle by a point mass. A more detailed simulation distinguishes between the 'location of the vehicle' and the 'location of the inertial platform.' The former may be defined by the location of either the center of mass c or an identifiable point fixed in the vehicle; the latter is specified by the coordinates of another fixed in the vehicle; the latter is specified by the coordinates of another fixed point o in the vehicle. Absolute locations are usually defined with respect to an inertial coordinate system. As the propellant is burned and mass particles ejected, the simulation keeps track of c by integrating the equation of a rocket. The simulated guidance system contains a 'guidance computer' which integrates the specific force outputs of the simulated accelerometers to obtain the location of the point o. The present objective is to write the simulation equations to a degree of detail which will produce sufficiently accurate absolute positions of the vehicle and platform to obtain a realistic value for their relative position. Thomson derives the equations of motion of a variable-mass system. The derivation is extended here to provide terms that are useful and convenient in solving the stated problem. The data that are given or assumed to be known from other parts of the simulation include the 'engine thrust,' the vehicle's angular velocity and a tabular time-history of the relative location of the c.m. which extends over staging intervals. (Author)
Equations of Motion for a Variable-Mass Inertially-Guided System
1967
4 pages
Report
No indication
English
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