1. Concerning the rolling disturbance caused by the joint work of a rocket carriers LPR Engines Boris Rabinovich

2. Concerning the rolling disturbance caused by the joint work of a rocket carriers LPR Engines The problem of the rolling disturbance moment is considered arising during the joint work of a lot of liquid propellant rocket engines (LPR Engines). The engines are supposed to be located on the equal distances along the circle as for example on the A-section of the heavy rocket carrier N-1. The simple mathematical models are proposed for the qualitative explanation of some phenomenon being observed during the flight experiments, namely: The arising of the disturbing moment around the longitudinal axis of the rocket caused by the twist of the joint work of all of the rocket engines. The absence of such a moment in the case of an interval in the working engines chain (two engines located on the opposite ends of the diameter are turned off). 2

3. The position of the LPRE NK-15 on the A-section of the rocket carrier N-1 3

4. a) Continuous chain of the LPRE, the regular symmetry b) The chain of LPRE having the gates (N-1 # 3L) c) Continuous chain of LPRE, the screw symmetry (N-1 # 6L) Equilibrium forms of the jets system 4

5. a) Continuous chain of the LPRE, the regular symmetry b) The chain of LPRE having the gates (N-1 # 3L) c) Continuous chain of LPRE, the screw symmetry (N-1 # 6L) Equilibrium forms of the jets system 5

6. The model of the LPRE chain having the gates (N-1 # 3L ) Non-symmetric equilibrium form Symmetric equilibrium form 6 The system of two cores

7. The model of the LPRE chain having the gates Potential energy (3) Equilibrium conditions (4) Stability conditions (5) Generalized coordinates (1) External forces (2) 7

8. The model of the LPRE chain having the gates The existence by k>>cl 2 is impossible Non-symmetric equilibrium form Symmetric equilibrium form The existence by k>>cl 2 is most probable Equilibrium conditions - (6), (8). Stability conditions - (7), (9 ) 8 The equilibrium forms and stability

9. The model of continuous LPRE chain (N-1 # 6L). The plane orthogonal to the longitudinal axis The plane passing through the longitudinal axis 9 One of the cores

10. The model of continuous LPRE chain Potential energy (11) Equilibrium conditions (12) Stability conditions (13) External forces (10) 10

11. The model of continuous LPRE chain The existence by k>>c l 2 is most probable The screw symmetry The existence by k>>c l 2 is impossible Equilibrium conditions – (14), (16). Stability conditions –(15), (17) 11 The regular symmetry

12. Concerning the rolling disturbance caused by the joint work of a rocket carriers LPR Engines The equilibrium forms of the jets system with the right-screw or left- screw symmetry are stable while absence of the gates in the LPRE chain. The jets axle are screwing in this case around the longitudinal axis of the rocket. The regular-symmetric form of the jets system equilibrium will transform immediately, being non-stable, in one of the equilibrium forms with the screw symmetry. The last one create the mighty disturbing rolling moment. This moment has been observed by the lunch of the N-1 rocket carrier # 6 L. In the case of the gates in the contrary the regular-symmetric equilibrium form of the jets system is stable. The jets neighboring to the gates have the inclination in the direction of the gates. The existence of non-symmetric equilibrium forms arising while absence of the gates is impossible in this case. The symmetric form of the jets system has been appeared probably by the N-1 rocket carrier # 3 L lunch. The disturbing rolling moment was in this case not observed. 12 Summary

13. a) Continuous chain of the LPRE, the regular symmetry b) The chain of LPRE having the gates(N-1 # 3L) c) Continuous chain of LPRE, the screw symmetry (N-1 # 6L) Equilibrium forms of the jets system 13

14. Concerning the rolling disturbance caused by the joint work of a rocket carriers LPR Engines Boris Rabinovich Space Research Institute (IKI) Russian Academy of Sciences Profsoyuznaya 84/32, Moscow 117810, Russia The electronic version vas fulfilled by Victoria Prokhorenko 14