USING A MOVING MASS TO CHANGE THE SPATIAL ORIENTATION OF A RIGID BODY SUBJECT TO TIME-DEPENDENT EXTERNAL FORCES

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Abstract

A mechanical system consisting of a rigid body and a material point is considered. They interact with each other by means of internal forces whose physical nature is not defined. Both objects are affected by external forces specified as functions of time. The task is to construct a trajectory for a point mass such that the solid body, under the action of the force of interaction with this mass, changes its orientation in space according to a predetermined program. Based on the theorem on the change in the relative moment of momentum, a second-order vector differential equation, unresolved with respect to the highest derivative, is obtained that describes the system. A change of variables is found that allows replacing the original equation with a first-order vector differential equation resolved with respect to the derivative. All special cases arising from the use of the new equation are considered. The obtained relationships can be used to control spacecraft and robotic systems.

About the authors

A. M. Shmatkov

Institute for Problems in Mechanics, RAS

Author for correspondence.
Email: shmatkov@ipmnet.ru
Moscow, Russia

References

  1. Xu J., Fang H. Improving performance: recent progress on vibration-driven locomotion systems // Nonlinear Dyn. 2019. V. 98. № 4. P. 2651–2669. https://doi.org/10.1007/s11071-019-04982-y
  2. Liu Y., Chernousko F.L., Terry B.S., Chávez J.P. Special issue on self-propelled robots: from theory to applications // Meccanica. 2023. V. 58. P. 317–319. https://doi.org/10.1007/s11012-022-01631-4
  3. Schmoeckel F., Worn H. Remotely controllable mobile microrobots acting as nano positioners and intelligent tweezers in scanning electron microscopes (SEMs) / Proceeding of international conference robotics and automation. 2001. IEEE, New York. P. 3903–3913.
  4. Lampert P., Vakebtutu A., Lagrange B., De Lit P., Delchambre A. Design and performances of a one-degree-of-freedom guided nano-actuator // Robot. Comput. Integr. Manuf. 2003. V. 19. № 1–2. P. 89–98. https://doi.org/10.1016/s0736-5845(02)00065-0
  5. Vartholomeos P., Papadopoulos E. Dynamics, design and simulation of a novel microrobotic platform employing vibration microactuators // J. Dyn. Syst. Meas. Control. 2006. V. 128. № 1. P. 122–133. https://doi.org/10.1115/1.2168472
  6. Gradetsky V., Solovtsov V., Kniazkov M., Rizzotto G.G., Amato P. Modular design of electromagnetic mechatronic microrobots / Proceedings of 6th international conference climbing and walking robots (CLAWAR). 2003. Catania, Italy. P. 651–658.
  7. Chernousko F.L. On the motion of a body containing movable internal mass // Dokl. Phys. 2005. V. 50. № 11. P. 593–597. https://doi.org/10.1134/1.2137795
  8. Bolotnik N.N., Figurina T.Yu., Chernousko F.L. Optimal control of the rectilinear motion of a two-body system in a resistive medium // J. Appl. Math. Mech. 2012. V. 76. № 1. P. 1–14. https://doi.org/10.1016/j.jappmathmech.2012.03.001
  9. Li H., Furuta K., Chernousko F.L. Motion generation of the Capsubot using internal force and static friction / Proceedings of the 45th IEEE conference on decision and control. 2006. San Diego, USA. P. 6575–6580. https://doi.org/10.1109/cdc.2006.377472
  10. Zimmerman K., Zeidis I., Bolotnik N., Pivovarov M. Dynamics of a two-module vibration-driven system moving along a rough horizontal plane // Multibody Syst. Dyn. 2009. V. 22. № 2. P. 199–219. https://doi.org/10.1007/s11044-009-9158-2
  11. Chernousko F.L. Two-dimensional motions of a body containing internal moving masses // Meccanica. 2016. V. 51. № 12. P. 3203–3209. https://doi.org/10.1007/s11012-016-0511-2
  12. Chernousko F.L. Optimal control of the motion of a double-mass system // Dokl. Math. 2018. V. 97. № 3. P. 295–299. https://doi.org/10.1134/s1064562418030195
  13. Shmatkov A.M. Time-optimal rotation of a body by displacement of a mass point // Dokl. Phys. 2018. V. 63. № 8. P. 337–341. https://doi.org/10.1134/s1028335818080062
  14. Bolotnik N., Figurina T. Controllabilty of a two-body crawling system on an inclined plane // Meccanica. 2023. V. 58. P. 321–336. https://doi.org/10.1007/s11012-021-01466-5
  15. Figurina T., Knyazkov D. Periodic regimes of motion of capsule system on rough plane // Meccanica. 2023. V. 58. P. 493–507. https://doi.org/10.1007/s11012-022-01572-y
  16. Chernousko F.L. Controlling the orientation of a solid using the internal mass // J. Appl. Mech. Tech. Phys. 2019. V. 60. № 2. P. 278–283. https://doi.org/10.1134/s0021894419020093
  17. Naumov N.Yu., Chernousko F.L. Reorientation of a rigid body controlled by a movable internal mass // J. Comput. Syst. Sci. Int. 2019. V. 58. № 2. P. 252–259. https://doi.org/10.1134/s106423071902014x
  18. Chernousko F. Reorientation of a rigid body by means of auxiliary masses // Meccanica. 2023. V. 58. P. 387–395. https://doi.org/10.1007/s11012-022-01501-z
  19. Shmatkov A.M. Objects changing the spatial orientation of a solid body by using mobile mass // J. Comput. Syst. Sci. Int. 2020. V. 59. № 4. P. 622–629. https://doi.org/10.1134/s1064230720040139
  20. Абезяев И.Н. Об одной возможности ориентации околоземного космического аппарата по магнитному полю земли // Изв. РАН. МТТ. 2022. № 6. С. 54–62. https://doi.org/10.31857/S0572329922050026
  21. Левский М.В. Кватернионное решение задачи оптимального управления ориентацией твердого тела (космического аппарата) с комбинированным критерием качества // Изв. РАН. МТТ. 2024. № 1. С. 197–222. https://doi.org/10.31857/S1026351924010115
  22. Белецкий В.В., Яншин А.М. Влияние аэродинамических сил на вращательное движение искусственных спутников. Киев: Наук. думк., 1984. 187 с.
  23. Заболотнов Ю.М., Назарова А.А., Ван Ч. Анализ динамики и управление при развертывании кольцевой тросовой группировки космических аппаратов // Изв. РАН. МТТ. 2023. № 4. С. 110–124. https://doi.org/10.31857/S0572329922600670
  24. Шматков А.М. Пространственная переориентация твердого тела посредством подвижной массы при наличии внешних сил, заданных как функции времени // ДАН. 2024. Т. 517. № 4. С. 59–64. https://doi.org/10.31857/S2686740024040098
  25. Shmatkov A.M. Changing the spatial orientation of a rigid body using one moving mass in the presence of external forces // Meccanica. 2023. V. 58. P. 441–450. https://doi.org/10.1007/s11012-022-01524-6
  26. Маркеев А.П. Теоретическая механика. М.: ЧеРо, 1999. 572 с.
  27. Журавлев В.Ф. Основы теоретической механики. М.: ФИЗМАТЛИТ, 2008. 304 с.

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