Pre and post orbit maneuver pulses to reduce flexural oscillations

1. A method for performing an orbital maneuver on a spacecraft by firing a thruster, the method comprising:

executing a first double pulse, double coast firing (DPDC) sequence with the thruster prior to the orbital maneuver;

firing the thruster for a duration of the orbital maneuver; and

executing a second DPDC firing sequence with the thruster subsequent to the orbital maneuver.

2. The method of claim 1 , wherein:

the first DPDC firing sequence includes a first pulse firing having a first duration T a1 , followed by a first coast interval having a second duration T b1 , followed by a second pulse firing for the second duration T b1 , followed by a second coast interval for the first duration T a1 ; and

the second DPDC firing sequence includes a third coast interval for a third duration T a2 , followed by a third pulse firing for a fourth duration T b2 , followed by a fourth coast interval for the fourth duration T b2 followed by a fourth pulse firing for the third duration Ta 2 .

3. The method of claim 1 , wherein:

the spacecraft includes, in an on-orbit configuration, a deployed appendage, mechanically coupled with the spacecraft and has a characteristic dynamic response period of oscillation (‘T’); and

each of T a1 , T b1 , T a2 , andT b2 is selected as a respective particular fraction of the characteristic dynamic response period.

4. The method of claim 3 , wherein T a1 and T a2 are selected to be within the approximate range of 0.06 T to 0.1 T and T b1 and T b2 are selected to be within the approximate range of 0.1 T to 0.3 T.

5. The method of claim 3 , wherein T a1 and T a2 are selected to be approximately equal to 0.08 T and T b1 and T b2 are selected to approximately equal 0.21 T.

6. The method of claim 3 , wherein T a1 and T a2 are selected to be approximately equal to 0.09 T and T b1 and T b2 are selected to be approximately equal 0.28 T.

7. The method of claim 3 , wherein T a1 =T a2 and T b1 =T b2 .

8. The method of claim 3 , wherein the appendage is a solar array or a payload element.

9. A spacecraft comprising a spacecraft controller and a thruster, the spacecraft controller configured to cause the spacecraft to execute an orbital maneuver by firing a thruster, wherein the spacecraft controller:

executes a first double pulse, double coast firing (DPDC) sequence with the thruster prior to the orbital maneuver;

fires the thruster for a duration of the orbital maneuver; and

executes a second DPDC firing sequence with the thruster subsequent to the orbital maneuver.

10. The spacecraft of claim 9 , wherein:

the first DPDC firing sequence includes a first pulse firing having a first duration T a1 , followed by a first coast interval having a second duration T b1 , followed by a second pulse firing for the second duration T b1 , followed by a second coast interval for the first duration T a1 ; and

the second DPDC firing sequence includes a third coast interval for a third duration T a2 , followed by a third pulse firing for a fourth duration T b2 , followed by a fourth coast interval for the fourth duration T b2 followed by a fourth pulse firing for the third duration Ta 2 .

11. The spacecraft of claim 9 , wherein:

the spacecraft includes, in an on-orbit configuration, a deployed appendage, mechanically coupled with the spacecraft and has a characteristic dynamic response period of oscillation (‘T’); and

each of T a1 , T b1 , T a2 , and T b2 is selected as a respective particular fraction of the characteristic dynamic response period.

12. The spacecraft of claim 11 , wherein T a1 and T a2 are selected to be within the approximate range of 0.06 T to 0.1 T and T b1 and T b2 are selected to be within the approximate range of 0.1 T to 0.3 T.

13. The spacecraft of claim 11 , wherein T a1 and T a2 are selected to be approximately equal to 0.08 T and T b1 and T b2 are selected to approximately equal 0.21 T.

14. The spacecraft of claim 11 , wherein T a1 and T a2 are selected to be approximately equal 0.09 T and T b1 and T b2 are selected to approximately equal 0.28 T.

15. The spacecraft of claim 11 , wherein T a1 =T a2 and T b1 =T b2 .

16. The spacecraft of claim 11 , wherein the appendage is a solar array or a payload element.

17. A non-transitory computer readable medium having software stored thereon, the software including instructions for causing a controller to:

cause a spacecraft, the spacecraft including the controller and a thruster, to execute an orbital maneuver by firing the thruster, wherein the firing the thruster includes:

executing a first double pulse, double coast firing (DPDC) sequence with the thruster prior to the orbital maneuver;

firing the thruster for a duration of the orbital maneuver; and

executing a second DPDC firing sequence with the thruster subsequent to the orbital maneuver.

18. The computer readable medium of claim 17 , wherein:

the first DPDC firing sequence includes a first pulse firing having a first duration T a1 , followed by a first coast interval having a second duration T b1 , followed by a second pulse firing for the second duration T b1 , followed by a second coast interval for the first duration T a1 ; and

the second DPDC firing sequence includes a third coast interval for a third duration T a2 , followed by a third pulse firing for a fourth duration T b2 , followed by a fourth coast interval for the fourth duration T b2 followed by a fourth pulse firing for the third duration T a2 .

19. The computer readable medium of claim 17 , wherein:

the spacecraft includes, in an on-orbit configuration, a deployed appendage, mechanically coupled with the spacecraft and has a characteristic dynamic response period of oscillation (‘T’); and

each of T a1 , T b1 , T a2 , and T b2 is selected as a respective particular fraction of the characteristic dynamic response period.

20. The computer readable medium of claim 19 , wherein T a1 =T a2 and T b1 =T b2 .