F

INSTANTANEOUS MOTOfl THRUST VKCTOfl INSTANTANEOUS MASS Of TKf SPACECRAFT

A OCULAR RATI OF TKf PRINCIPAL AKES MTH RESFfCT TO INERTIAL SPACI

CHANGE Ā«INDUCED BV F11N T WE THAMSLATtOMAL VELOCITY OF TK1 SPACICRAFT CENTER OF MASS IN WIRTIAL SPACE

IOf AL VELOCITY CORRECTION WHICH mOUD BE PROOUCCD IN TH1 ASSaNCCOF OF MISALIGNMENTS AND NUTATION

ATTITUOl OUATKRNION IN INIRTEAL SPACt

SPACICRAFT ANGULAR MOMENTUM ABOUT ITS CENTIR OF MASS MOMENT OF INERTIA QVAOIC OF TMt SPACt CRAFT ABOUT ITS CENTIR OF MASS TOROUt ON THI SPACICRAFT ABOUT ITS CINTCR OF MASS

VICTOR FROM THK SPACECRAFT CENTER OF MASS TO A SCLECTEOPOINT ON THE LINE OF ACTION OF P ill DAMPING TOnOUC

Fig. 17-7. Summary of the Dynamics Equations for Modeling Torques Due to Orbit Maneuvers. All vector quantities are resolved along spacecraft principal axes.

about 1.6 kg out of a total fuel budget of 11.2 kg for fine orbit correction maneuvers. The simulation runs with 10 times the nominal specified misalignments-indicated that the effects would be 10 times larger: In view of the above results, the spacecraft hardware was aligned with extra care so that all the misalignments were within the nominal specified limits.

17.4.2 Thrust Vector Not Collinear With Spin Axis but Nominally Passing Through Spacecraft Center of Mass

This configuration is used for small velocity changes, where it is possible to tolerate some fuel wastage. In this configuration, the engine must be fired in a pulsed mode so that a net thrust in the desired direction is generated.

As the fuel is used, the spacecraft center of mass will move on the spin axis. The thrust vector will not always pass through the center of mass of the spacecraft and hence a torque will be generated which will cause the spacecraft to precess and nutate.

The effect of misalignments can be modeled similarly to that for the first configuration, the main difference being in the modeling of the angular momentum of the exhaust gases, because for small rocket engines, a liquid or gas fuel is normally used. This fuel must be moved from storage tanks to the engine before use, resulting in a change in the spacecraft moments of inertia before engine firing. In addition, the engine firing in a pulsed mode must be modeled.

References

1. Abramson, H. N., W. H. Chu, and G. E. Ramsleben, Jr., "Representation of Fuel Sloshing in Cylindrical Tanks by an Equivalent Mechanical Model," Am. Rocket Society J., Vol. 31, p. 1967-1705, 1961.

2. Abramson, H. N., editor, The Dynamic Behavior of Liquids in Moving Containers, NASA SP-106, 1966.

AV O'iFf RINTlAl EQUATIONS

1U1IA SVWMtlRIC PARAMtltR OlfflRtMltAl. I OU AT ION IQI Ol H l-il

AttCUlAR RATI ALGEBRAIC CQUATION

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