DEVELOPING THE RESEARCH LINES OF VIKTOR V. PYLYPENKO, AN ACADEMICIAN OF THE NATIONAL ACADEMY OF SCIENCES OF UKRAINE: For the 90th birth anniversary of Viktor V. Pylypenko, an Academician of the National Academy of Sciences of Ukraine
This paper presents the results of studies along the principal research lines of Viktor V. Pylypenko, an Academician of the National Academy of Sciences of Ukraine, obtained by his pupils over the recent years. The following lines are considered: the development of a theory of cavitation oscillation...
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liquid-propellant rocket engine cavitation oscillations low-frequency dynamic processes liquid-propellant launch vehicle pogo oscillations solid-propellant rocket engine pneumatic vibration protection system well drilling. |
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DOLGOPOLOV, S. I. NIKOLAYEV, O. D. KHORIAK, N. V. |
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DOLGOPOLOV, S. I. NIKOLAYEV, O. D. KHORIAK, N. V. DEVELOPING THE RESEARCH LINES OF VIKTOR V. PYLYPENKO, AN ACADEMICIAN OF THE NATIONAL ACADEMY OF SCIENCES OF UKRAINE: For the 90th birth anniversary of Viktor V. Pylypenko, an Academician of the National Academy of Sciences of Ukraine |
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DOLGOPOLOV, S. I. NIKOLAYEV, O. D. KHORIAK, N. V. |
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DOLGOPOLOV, S. I. |
| title |
DEVELOPING THE RESEARCH LINES OF VIKTOR V. PYLYPENKO, AN ACADEMICIAN OF THE NATIONAL ACADEMY OF SCIENCES OF UKRAINE: For the 90th birth anniversary of Viktor V. Pylypenko, an Academician of the National Academy of Sciences of Ukraine |
| title_short |
DEVELOPING THE RESEARCH LINES OF VIKTOR V. PYLYPENKO, AN ACADEMICIAN OF THE NATIONAL ACADEMY OF SCIENCES OF UKRAINE: For the 90th birth anniversary of Viktor V. Pylypenko, an Academician of the National Academy of Sciences of Ukraine |
| title_full |
DEVELOPING THE RESEARCH LINES OF VIKTOR V. PYLYPENKO, AN ACADEMICIAN OF THE NATIONAL ACADEMY OF SCIENCES OF UKRAINE: For the 90th birth anniversary of Viktor V. Pylypenko, an Academician of the National Academy of Sciences of Ukraine |
| title_fullStr |
DEVELOPING THE RESEARCH LINES OF VIKTOR V. PYLYPENKO, AN ACADEMICIAN OF THE NATIONAL ACADEMY OF SCIENCES OF UKRAINE: For the 90th birth anniversary of Viktor V. Pylypenko, an Academician of the National Academy of Sciences of Ukraine |
| title_full_unstemmed |
DEVELOPING THE RESEARCH LINES OF VIKTOR V. PYLYPENKO, AN ACADEMICIAN OF THE NATIONAL ACADEMY OF SCIENCES OF UKRAINE: For the 90th birth anniversary of Viktor V. Pylypenko, an Academician of the National Academy of Sciences of Ukraine |
| title_sort |
developing the research lines of viktor v. pylypenko, an academician of the national academy of sciences of ukraine: for the 90th birth anniversary of viktor v. pylypenko, an academician of the national academy of sciences of ukraine |
| description |
This paper presents the results of studies along the principal research lines of Viktor V. Pylypenko, an Academician of the National Academy of Sciences of Ukraine, obtained by his pupils over the recent years. The following lines are considered: the development of a theory of cavitation oscillations in liquid-propellant rocket engine (LPRE) pumps, the study of low-frequency dynamics in liquid-propellant rocket propulsion systems (LPRPSs), the analysis and assurance of liquid-propellant launch vehicle pogo stability, the mathematical simulation of dynamic processes in solid-propellant rocket engines, the development of pneumatic vibration protection modules, and the improvement of drilling technology by using cavitation hydrovibrator. A hydrodynamic model of cavitating LPRE pumps was developed further: it was verified using theoretical and experimental transfer matrices of cavitating pumps, and two new coefficients were introduced: the time of disturbance transfer delay due to the presence of cavities and the cavitation resistance distribution coefficient; from the results of dynamic tests of 26 pumps, the cavity elasticity was determined for pumps with extended ranges of their geometric parameters and operating conditions; a pump choking mechanism was developed, and it was shown that the pump choking characteristic is a specific nonlinearity involving a critical cavity flow; a mechanism of hard excitation of cavitation self-oscillations was proposed, and they were mathematically simulated. A theory of LPRPS low-frequency dynamics was developed further: procedures were developed for determining the effect of a nonsimultaneous engine startup and external and internal factors on LPRE startup thrust spread; a mathematical simulation was conducted to study sustainer engine startup and shutdown transients in the common feed system of the sustainer engine and the liquid-propellant thrust system of the Cyclone-4M launch vehicle’s upper stage. A study was conducted on pogo vibrations in the prototype Cyclone and Dnipro launch vehicles unstable for pogo vibrations during the first-stage engine operation.
REFERENCES
1. Pylypenko O. V., Dovgotko N. I. Outstanding scientist in mechanics Viktor Vassilievich Pylypenko. Teh. Meh. 2015. No. 4. Pp. 3-22. (In Russian).
2. Dolgopolov S. I. Verification of a hydrodynamic model of a liquid-propellant rocket engine's cavitating pumps using experimental and theoretical pump transfer matrices. Teh. Meh. 2020. No. 3. Pp. 18-28. (In Ukrainian).https://doi.org/10.15407/itm2020.03.018
3. Brennen C. E., Meissner C., Lo E. Y., Hoffman G. S. Scale effects in the dynamic transfer functions for cavitating inducers. Journal of Fluids Engineering. 1982. V. 104. No. 4. Pp. 428-433.https://doi.org/10.1115/1.3241875
4. Pylypenko V. V., Kvasha Yu. A. Stability of cavity flow past a plate cascade. Teh. Meh. 2001. No. 2. Pp. 144-149. (In Russian).
5. Dolgopolov S. I. Determining the coefficients of a hydrodynamic model of cavitating pumps of liquid-propellant rocket engines from their theoretical transfer matrices. Teh. Meh. 2024. No. 1. Pp. 16 - 25. (In Ukrainian). https://doi.org/10.15407/itm2024.01.016
6. Dolgopolov S. I. Generalization of experimental elasticity of cavitation bubbles in LRE pumps that differ significantly in size and performance. Science and Innovation. 2023. V. 19. No. 19(5). Pp. 71 - 88.
7. Dolgopolov S. I. Experiment-and-calculation determination of the coefficients appearing in a mathematical model of cavitating pumps of liquid-propellant rocket engines. Teh. Meh. 2024. No. 3. Pp. 67 - 85. (in Ukrainian).https://doi.org/10.15407/itm2024.03.067
8. Dolgopolov S. I. Mathematical simulation of choking under self-oscillations in hydraulic systems with cavitating pumps of liquid-propellant rocket engines. Teh. Meh. 2020. No. 4. Pp. 35 - 42. (in Ukrainian).https://doi.org/10.15407/itm2020.04.035
9. Dolgopolov S. I. Mathematical simulation of hard excitation of cavitation self-oscillations in a liquid-propellant rocket engine feed system. Teh. Meh. 2021. No. 1. Pp. 29 - 36. (in Ukrainian).https://doi.org/10.15407/itm2021.01.029
10. Pylypenko O. V., Dolhopolov S. I., Nikolayev O. D., Khoriak N. V. Mathematical simulation of the start of a multiengine liquid-propellant rocket propulsion system. Teh. Meh. 2020. No. 1. Pp. 5 - 18. (In Russian).https://doi.org/10.15407/itm2020.01.005
11. Dolgopolov S., Nikolayev O., Khoriak N. Dynamic interaction between clustered liquid propellant rocket engines under their asynchronous start-ups. Propulsion and Power Research. 2021. V. 10. No. 4. Pp. 347 - 359.https://doi.org/10.1016/j.jppr.2021.12.001
12. Pylypenko O. V., Prokopchuk O. O., Dolgopolov S. I., Nikolayev O. D., Khoriak N. V., Pysarenko V. Yu., Bashliy I. D., Polskykh S. V. Mathematical modeling of start-up transients at clustered propulsion system with POGO-suppressors for Cyclon-4M launch vehicle. Space Science and Technology. 2021. V. 27. No. 6 (133). Pp. 3 - 15.https://doi.org/10.15407/knit2021.06.003
13. Pylypenko O. V., Dolgopolov S. I., Khoriak N. V., Nikolayev O. D. Procedure for determining the effect of internal and external factors on the startup thrust spread of a liquid-propellant rocket engine. Teh. Meh. 2021. No. 4. Pp. 7 - 17. (In Ukrainian).https://doi.org/10.15407/itm2021.04.007
14. Dolgopolov S. I. Determination of the effect of internal and external factors on the thrust spread of a cluster propulsion system. Teh. Meh. 2022. No. 2. Pp. 47 - 58. (In Ukrainian).https://doi.org/10.15407/itm2022.02.047
15. Pylypenko O. V., Dolgopolov S. I., Nikolayev O. D., KhoriaN. V., Kvasha Yu. A., Bashliy I. D. Determination of the thrust spread in the Cyclone-4M first stage multi-engine propulsion system during its start. Science and Innovation. 2022. V. 18. No. 6. Pp. 97 - 112.
16. Pylypenko O. V., Nikolayev O. D., Bashliy I. D., Dolgopolov S. I. Mathematical modeling of dynamic processes in feeding system of space stage main engine of launch vehicle at active and passive flight. Space Science and Technology. 2020. V. 26. No. 1. Pp. 3 - 17. (In Russian).https://doi.org/10.15407/knit2020.01.003
17. Pylypenko O. V., Smolenskyy D. E., Nikolayev O. D., Bashliy I. D. The approach to numerical simulation of the spatial movement of fluid with forming free gas inclusions in propellant tank at space flight conditions. Space Science and Technology. 2022. V. 28. No. 5. Pp. 3 - 14.https://doi.org/10.15407/knit2022.05.003
18. Pylypenko O. V., Nikolayev O. D., Bashliy I. D., Zavoloka O. M. Approach to numerical simulation of the spatial motions of a gas/liquid medium in a space stage propellant tank in microgravity with account for the hot zone. Teh. Meh. 2022. No. 4. Pp. 3 - 15. (In Ukrainian).https://doi.org/10.15407/itm2022.04.003
19. Nikolayev O. D., Bashliy I. D., Sviridenko N. F., Khoriak N. V. Determination of the parameters of motion of the gas-liquid interface in the fuel tanks of launch vehicle space stages in passive portions of the flight. Teh. Meh. 2017. No. 4. Pp. 26 - 40. (In Russian).https://doi.org/10.15407/itm2017.04.026
20. Pylypenko O. V., Dolgopolov S. I., Nikolayev O. D., Khoriak N. V. Mathematical modeling of the transient processes in propulsion system of the upper stage of the Cyclone-4M launch vehicle. Science and Innovation. 2024. V. 20. No. 1. Pp. 49 - 67.
21. Pylypenko O. V., Nikolayev O. D., Bashliy I. D., Khoriak N. V. Approach to the POGO stability analysis of a liquid-propellant "core and strap-on boosters" launch vehicle. Teh. Meh. 2022. No. 3. Pp. 3 - 15. (In Ukrainian).https://doi.org/10.15407/itm2022.03.003
22. Pylypenko O. V., Degtyarev M. A., Nikolayev O. D., Klimenko D. V., Dolgopolov S. I., Khoriak N. V., Bashliy I. D., Silkin L. A. Providing of POGO stability of the Cyclone-4M launch vehicle. Space Science and Technology. 2020. V. 26. No. 4 (125). Pp. 3 - 20.https://doi.org/10.15407/knit2020.04.003
23. Nikolayev O. D., Bashliy I. D., Khoryak N. V. Сomputation of the POGO self-oscillation parameters in dynamic "propulsion - rocket structure" system by using of 3D structural model. Teh. Meh. 2018. No. 2. Рp. 17 - 29.https://doi.org/10.15407/itm2018.02.017
24. Nikolaev A. D., Khoryak N. V., Serenko V. A., Klimenko D. V., Khodorenko V. F., Bashliy I. D. Considering dissipative forces for mathematical modeling longitudinal vibrations of liquid launch vehicle body. Teh. Meh. 2016. No. 2. Pp. 16 - 31. (In Russian).
25. Dolgopolov S., Nikolayev O. Features of mathematical modeling of nonlinear Pogo oscillations of launch vehicles. CEAS Space Journal. 2024. V. 16. Iss. 2. Pp. 32 - 48.https://doi.org/10.1007/s12567-024-00541-3
26. Pylypenko O. V., Dolgopolov S. I., Khoriak N. V., Nikolayev O. D. Evaluation of the scatter of liquid launch vehicle POGO oscillation amplitudes due to the influence of the scatter of internal factors. Space Science and Technology. 2024. V. 30. No. 3 (148). Pp. 3-15.https://doi.org/10.15407/knit2024.03.003
27. Nikolayev O. D., Bashliy I. D., Khoriak N. V., Bondarenko S. H. Effect of the surface roughness of a power plant chamber on low-frequency self-oscillations of a cold working gas. Teh. Meh. 2023. No. 3. Pp. 3 - 17. (In Ukrainian).https://doi.org/10.15407/itm2023.03.003
28. Bashlii I., Nikolayev O., Marchan R. Low-frequency oscillations of combustion products in the chamber of a low-thrust liquid rocket engine manufactured using additive technologies. Aerospace Technic and Technology. 2024. No. 4sup1. Pp. 60-68. (In Ukrainian).
29. Dolgopolov S. I., Nikolayev O. D. Development of an approach to mathematical simulation of dynamic processes in a solid-propellant rocket engine. Teh. Meh. 2024. No. 4. Pp. 10-16. (In Ukrainian).https://doi.org/10.15407/itm2024.04.010
30. Nikolaev O. D., Bashliy I. D., Klymenko D. V., Khoriak N. V. Interaction of the acoustic oscillations of the combustion products in the chamber of a propulsion system with structural vibrations. Teh. Meh. 2025. No. 1. Pp. 3- 17. (In Ukrainian).https://doi.org/10.15407/itm2025.01.028
31. Nikolaev O. D., Bashliy I. D., Sukachevskyi V. O. Features of the development of acoustic oscillations in the combustion product flow in power plant chambers when using propellant components derived from lunar regolith. Teh. Meh. 2025. No. 2. Pp. 3-16. (In Ukrainian).https://doi.org/10.15407/itm2025.02.003
32. Pylypenko M. V. System for space hardware vibration protection in transportation. Teh. Meh. 2020. No. 1. Pp. 120-130. (In Ukrainian).https://doi.org/10.15407/itm2020.01.120
33. Nikolayev D. O., Khoroshylov S. V. Prediction of dynamic loads on spacecraft in the active light of the launch vehicle using the results of liquid-propellant rocket engine fire tests. Teh. Meh. 2024. No. 1. Pp. 3-15. (In Ukrainian).https://doi.org/10.15407/itm2024.01.003
34. Nikolayev O., Zhulay Yu., Kvasha Yu., Dzoz N. Determination of the vibration accelerations of drill bits with the rotative-vibration well drilling method using the cavitation hydrovibrator. Int. J. Mining and Mineral Engineering. 2020. V. 11. No. 2. Pp. 102-120. https://doi.org/10.1504/IJMME.2020.108643
35. Zhulay Yu. O., Nikolaev O. D. Results of testing and modelling the "drilling rig with hydraulic vibrator - rock" system. Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu. 2020. No. 1. Pp. 11-17.https://doi.org/10.33271/nvngu/2020-1/011
36. Zhulay Yu. O., Nikolayev O. D. Evaluation of hydraulic power of drilling string with a cavitation hydrovibrator. Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu. 2021. No. 3. Pp. 31-37.https://doi.org/10.33271/nvngu/2021-3/031
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2025 |
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oai:ojs2.journal-itm.dp.ua:article-1502025-12-12T21:23:48Z DEVELOPING THE RESEARCH LINES OF VIKTOR V. PYLYPENKO, AN ACADEMICIAN OF THE NATIONAL ACADEMY OF SCIENCES OF UKRAINE: For the 90th birth anniversary of Viktor V. Pylypenko, an Academician of the National Academy of Sciences of Ukraine DOLGOPOLOV, S. I. NIKOLAYEV, O. D. KHORIAK, N. V. liquid-propellant rocket engine, cavitation oscillations, low-frequency dynamic processes, liquid-propellant launch vehicle pogo oscillations, solid-propellant rocket engine, pneumatic vibration protection system, well drilling. This paper presents the results of studies along the principal research lines of Viktor V. Pylypenko, an Academician of the National Academy of Sciences of Ukraine, obtained by his pupils over the recent years. The following lines are considered: the development of a theory of cavitation oscillations in liquid-propellant rocket engine (LPRE) pumps, the study of low-frequency dynamics in liquid-propellant rocket propulsion systems (LPRPSs), the analysis and assurance of liquid-propellant launch vehicle pogo stability, the mathematical simulation of dynamic processes in solid-propellant rocket engines, the development of pneumatic vibration protection modules, and the improvement of drilling technology by using cavitation hydrovibrator. A hydrodynamic model of cavitating LPRE pumps was developed further: it was verified using theoretical and experimental transfer matrices of cavitating pumps, and two new coefficients were introduced: the time of disturbance transfer delay due to the presence of cavities and the cavitation resistance distribution coefficient; from the results of dynamic tests of 26 pumps, the cavity elasticity was determined for pumps with extended ranges of their geometric parameters and operating conditions; a pump choking mechanism was developed, and it was shown that the pump choking characteristic is a specific nonlinearity involving a critical cavity flow; a mechanism of hard excitation of cavitation self-oscillations was proposed, and they were mathematically simulated. A theory of LPRPS low-frequency dynamics was developed further: procedures were developed for determining the effect of a nonsimultaneous engine startup and external and internal factors on LPRE startup thrust spread; a mathematical simulation was conducted to study sustainer engine startup and shutdown transients in the common feed system of the sustainer engine and the liquid-propellant thrust system of the Cyclone-4M launch vehicle’s upper stage. A study was conducted on pogo vibrations in the prototype Cyclone and Dnipro launch vehicles unstable for pogo vibrations during the first-stage engine operation. REFERENCES 1. Pylypenko O. V., Dovgotko N. I. Outstanding scientist in mechanics Viktor Vassilievich Pylypenko. Teh. Meh. 2015. No. 4. Pp. 3-22. (In Russian). 2. Dolgopolov S. I. Verification of a hydrodynamic model of a liquid-propellant rocket engine's cavitating pumps using experimental and theoretical pump transfer matrices. Teh. Meh. 2020. No. 3. Pp. 18-28. (In Ukrainian).https://doi.org/10.15407/itm2020.03.018 3. Brennen C. E., Meissner C., Lo E. Y., Hoffman G. S. Scale effects in the dynamic transfer functions for cavitating inducers. Journal of Fluids Engineering. 1982. V. 104. No. 4. Pp. 428-433.https://doi.org/10.1115/1.3241875 4. Pylypenko V. V., Kvasha Yu. A. Stability of cavity flow past a plate cascade. Teh. Meh. 2001. No. 2. Pp. 144-149. (In Russian). 5. Dolgopolov S. I. Determining the coefficients of a hydrodynamic model of cavitating pumps of liquid-propellant rocket engines from their theoretical transfer matrices. Teh. Meh. 2024. No. 1. Pp. 16 - 25. (In Ukrainian). https://doi.org/10.15407/itm2024.01.016 6. Dolgopolov S. I. Generalization of experimental elasticity of cavitation bubbles in LRE pumps that differ significantly in size and performance. Science and Innovation. 2023. V. 19. No. 19(5). Pp. 71 - 88. 7. Dolgopolov S. I. Experiment-and-calculation determination of the coefficients appearing in a mathematical model of cavitating pumps of liquid-propellant rocket engines. Teh. Meh. 2024. No. 3. Pp. 67 - 85. (in Ukrainian).https://doi.org/10.15407/itm2024.03.067 8. Dolgopolov S. I. Mathematical simulation of choking under self-oscillations in hydraulic systems with cavitating pumps of liquid-propellant rocket engines. Teh. Meh. 2020. No. 4. Pp. 35 - 42. (in Ukrainian).https://doi.org/10.15407/itm2020.04.035 9. Dolgopolov S. I. Mathematical simulation of hard excitation of cavitation self-oscillations in a liquid-propellant rocket engine feed system. Teh. Meh. 2021. No. 1. Pp. 29 - 36. (in Ukrainian).https://doi.org/10.15407/itm2021.01.029 10. Pylypenko O. V., Dolhopolov S. I., Nikolayev O. D., Khoriak N. V. Mathematical simulation of the start of a multiengine liquid-propellant rocket propulsion system. Teh. Meh. 2020. No. 1. Pp. 5 - 18. (In Russian).https://doi.org/10.15407/itm2020.01.005 11. Dolgopolov S., Nikolayev O., Khoriak N. Dynamic interaction between clustered liquid propellant rocket engines under their asynchronous start-ups. Propulsion and Power Research. 2021. V. 10. No. 4. Pp. 347 - 359.https://doi.org/10.1016/j.jppr.2021.12.001 12. Pylypenko O. V., Prokopchuk O. O., Dolgopolov S. I., Nikolayev O. D., Khoriak N. V., Pysarenko V. Yu., Bashliy I. D., Polskykh S. V. Mathematical modeling of start-up transients at clustered propulsion system with POGO-suppressors for Cyclon-4M launch vehicle. Space Science and Technology. 2021. V. 27. No. 6 (133). Pp. 3 - 15.https://doi.org/10.15407/knit2021.06.003 13. Pylypenko O. V., Dolgopolov S. I., Khoriak N. V., Nikolayev O. D. Procedure for determining the effect of internal and external factors on the startup thrust spread of a liquid-propellant rocket engine. Teh. Meh. 2021. No. 4. Pp. 7 - 17. (In Ukrainian).https://doi.org/10.15407/itm2021.04.007 14. Dolgopolov S. I. Determination of the effect of internal and external factors on the thrust spread of a cluster propulsion system. Teh. Meh. 2022. No. 2. Pp. 47 - 58. (In Ukrainian).https://doi.org/10.15407/itm2022.02.047 15. Pylypenko O. V., Dolgopolov S. I., Nikolayev O. D., KhoriaN. V., Kvasha Yu. A., Bashliy I. D. Determination of the thrust spread in the Cyclone-4M first stage multi-engine propulsion system during its start. Science and Innovation. 2022. V. 18. No. 6. Pp. 97 - 112. 16. Pylypenko O. V., Nikolayev O. D., Bashliy I. D., Dolgopolov S. I. Mathematical modeling of dynamic processes in feeding system of space stage main engine of launch vehicle at active and passive flight. Space Science and Technology. 2020. V. 26. No. 1. Pp. 3 - 17. (In Russian).https://doi.org/10.15407/knit2020.01.003 17. Pylypenko O. V., Smolenskyy D. E., Nikolayev O. D., Bashliy I. D. The approach to numerical simulation of the spatial movement of fluid with forming free gas inclusions in propellant tank at space flight conditions. Space Science and Technology. 2022. V. 28. No. 5. Pp. 3 - 14.https://doi.org/10.15407/knit2022.05.003 18. Pylypenko O. V., Nikolayev O. D., Bashliy I. D., Zavoloka O. M. Approach to numerical simulation of the spatial motions of a gas/liquid medium in a space stage propellant tank in microgravity with account for the hot zone. Teh. Meh. 2022. No. 4. Pp. 3 - 15. (In Ukrainian).https://doi.org/10.15407/itm2022.04.003 19. Nikolayev O. D., Bashliy I. D., Sviridenko N. F., Khoriak N. V. Determination of the parameters of motion of the gas-liquid interface in the fuel tanks of launch vehicle space stages in passive portions of the flight. Teh. Meh. 2017. No. 4. Pp. 26 - 40. (In Russian).https://doi.org/10.15407/itm2017.04.026 20. Pylypenko O. V., Dolgopolov S. I., Nikolayev O. D., Khoriak N. V. Mathematical modeling of the transient processes in propulsion system of the upper stage of the Cyclone-4M launch vehicle. Science and Innovation. 2024. V. 20. No. 1. Pp. 49 - 67. 21. Pylypenko O. V., Nikolayev O. D., Bashliy I. D., Khoriak N. V. Approach to the POGO stability analysis of a liquid-propellant "core and strap-on boosters" launch vehicle. Teh. Meh. 2022. No. 3. Pp. 3 - 15. (In Ukrainian).https://doi.org/10.15407/itm2022.03.003 22. Pylypenko O. V., Degtyarev M. A., Nikolayev O. D., Klimenko D. V., Dolgopolov S. I., Khoriak N. V., Bashliy I. D., Silkin L. A. Providing of POGO stability of the Cyclone-4M launch vehicle. Space Science and Technology. 2020. V. 26. No. 4 (125). Pp. 3 - 20.https://doi.org/10.15407/knit2020.04.003 23. Nikolayev O. D., Bashliy I. D., Khoryak N. V. Сomputation of the POGO self-oscillation parameters in dynamic "propulsion - rocket structure" system by using of 3D structural model. Teh. Meh. 2018. No. 2. Рp. 17 - 29.https://doi.org/10.15407/itm2018.02.017 24. Nikolaev A. D., Khoryak N. V., Serenko V. A., Klimenko D. V., Khodorenko V. F., Bashliy I. D. Considering dissipative forces for mathematical modeling longitudinal vibrations of liquid launch vehicle body. Teh. Meh. 2016. No. 2. Pp. 16 - 31. (In Russian). 25. Dolgopolov S., Nikolayev O. Features of mathematical modeling of nonlinear Pogo oscillations of launch vehicles. CEAS Space Journal. 2024. V. 16. Iss. 2. Pp. 32 - 48.https://doi.org/10.1007/s12567-024-00541-3 26. Pylypenko O. V., Dolgopolov S. I., Khoriak N. V., Nikolayev O. D. Evaluation of the scatter of liquid launch vehicle POGO oscillation amplitudes due to the influence of the scatter of internal factors. Space Science and Technology. 2024. V. 30. No. 3 (148). Pp. 3-15.https://doi.org/10.15407/knit2024.03.003 27. Nikolayev O. D., Bashliy I. D., Khoriak N. V., Bondarenko S. H. 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