On the approximation of the field of attraction of a rigid body by the field of attraction of four material points of the same mass
DOI:
https://doi.org/10.21638/spbu01.2024.211Abstract
The problem of approximation of the gravitational potential of a rigid body by the potential of a system of four identical point masses is studied. Considering the potential in the form of expansion by a parameter characterizing the ratio of the mean body size to the distance to the test point of space, an approach is proposed to construct an approximate expression up to the terms of the third order of smallness. This approach is used to construct a model of the field of attraction for the comet nucleus (67P)Churyumov - Gerasimenko.Keywords:
moments of inertia of a rigid body, approximation of the potential of attraction, comet (67P)Churyumov - Gerasimenko
Downloads
Download data is not yet available.
References
Литература
1. Раус Э. Дж. Динамика системы твердых тел. Т. 1. Москва, Наука (1983).
2. Routh E. J. The elementary part of a treatise on the dynamics of a system of rigid bodies: Being Part I. of a treatise on the whole subject. London, Macmillan & Co (1891).
3. Дубошин Г. Н. Небесная механика. Основные задачи и методы. Москва, Наука (1968).
4. Кошляков Н. С., Глинер Э. Б., Смирнов М. М. Уравнения в частных производных математическойфизики. Москва, Высшая школа (1970).
5. Dobrovolskis A. R. Inertia of Any Polyhedron. Icarus 124 (2), 698-704 (1996). https://doi.org/10.1006/icar.1996.0243
6. Лурье А. И. Аналитическая механика. Москва, Госфизмат (1961).
7. Kennedy J., Eberhart R. Particle swarm optimization. Proceedings of ICNN’95 - International Conference on Neural Networks, Perth, WA, Australia 4, 1942-1948 (1995). https://doi.org/10.1109/ICNN.1995.488968
8. Poli R., Kennedy J., Blackwell T. Particle swarm optimization: an overview. Swarm Intelligence 1, 33-57 (2007). https://doi.org/10.1007/s11721-007-0002-0
9. Никонова Е. А. Равногранный тетраэдр и система точечных масс, равномоментная твердому телу. Вестник Санкт-Петербургского университета. Математика. Механика. Астрономия 10 (1), 155-164 (2023). https://doi.org/10.21638/spbu01.2023.113
10. Gaskell R., Jorda L., Capanna C., Hviid S., Gutierrez P. SPC SHAP5 CARTESIAN PLATE MODEL FOR COMET 67P/C-G 6K PLATES, RO-C-MULTI-5-67P-SHAPE-V2.0:CG_SPC_SHAP5_006K_CART, NASA Planetary Data System and ESA Planetary Science Archive (2017).
11. Буров А. А., Никонов В. И. Вычисление потенциала притяжения астероида (433) Эрос с точностью до членов четвертого порядка. Доклады Российской Академии наук. Физика, технические науки 492 (1), 58-62 (2020). https://doi.org/10.31857/S2686740020030086
12. Буров А. А., Никонов В. И. Чувствительность значенийкомпонент тензоров Эйлера - Пуансо к выбору триангуляционной сетки поверхности тела. Журнал вычислительной математики и математической физики 60 (10), 1764-1776 (2020). https://doi.org/10.31857/S0044466920100063
13. Burov A. A., Nikonov V. I. Inertial characteristics of higher orders and dynamics in a proximity of a small celestial body. Russian Journal of Nonlinear Dynamics 16 (2), 259-273 (2020). https://doi.org/10.20537/nd200203
14. Werner R. A. The gravitational potential of a homogeneous polyhedron or don’t cut corners. Celestial Mechanics and Dynamical Astronomy 59 (3), 253-278 (1994). https://doi.org/10.1007/BF00692875
15. Werner R. A., Scheeres D. J. Exterior gravitation of a polyhedron derived and compared with harmonic and mascon gravitation representations of asteroid 4769 Castalia. Celestial Mechanics and Dynamical Astronomy 65 (3), 313-344 (1996). https://doi.org/10.1007/BF00053511
16. Franklin Ph. Equimomental systems. Studies in Applied Mathematics 8 (1-4), 129-140 (1929).
17. Sommerville D. M. Y. Equimomental tetrads of a rigid body. Math. Notes 26, 10-11 (1930). https://doi.org/10.1017/S1757748900002127
18. Talbot A. Equimomental systems. The Mathematical Gazette 36 (316), 95-110 (1952). https://doi.org/10.2307/3610326
19. Huang N. C. Equimomental system of rigidly connected equal particles. Journal of Guidance, Control, and Dynamics 16 (6), 1194-1196 (1993). https://doi.org/10.2514/3.21150
20. Gil Chica F. J., P´erez Polo M., P´erez Molina M. Note on an apparently forgotten theorem about solid rigid dynamics. European Journal of Physics 35 (4), art. 045003 (2014). https://doi.org/10.1088/0143-0807/35/4/045003
21. Chaudhary H., Saha S. K. Balancing of shaking forces and shaking moments for planar mechanisms using the equimomental systems. Mechanism and Machine Theory 43 (3), 310-334 (2008). https://doi.org/10.1016/j.mechmachtheory.2007.04.003
22. Selig J. M. Geometric Fundamentals of Robotics. 2nd ed. Berlin, Springer (2005).
23. Selig J. M. Equimomental systems and robot dynamics. IMA Mathematics of Robotics, Sept. 9-11, 2015. Oxford, St Anne’s College (2015).
24. Laus L. P., Selig J. M. Rigid body dynamics using equimomental systems of point-masses. Acta Mechanica 231, 221-236 (2020). https://doi.org/10.1007/s00707-019-02543-3
25. Nu˜nez N. N. R., Vieira R. S., Martins D. Equimomental systems representations of point-masses of planar rigid-bodies. Acta Mechanica 234, 5565-5580 (2023). https://doi.org/10.1007/s00707-023-03683-3
References
1. Routh E. J. Dynamics of a system of rigid bodies. Vol. 1. Transl. from English. Moscow, Nauka Publ. (1983). (In Russian)
2. Routh E. J. The elementary part of a treatise on the dynamics of a system of rigid bodies: Being Part I. of a treatise on the whole subject. London, Macmillan & Co. (1891).
3. Duboshin G. N. Celestial Mechanics. Fundamental Problems and Methods. Moscow, Nauka Publ. (1968). (In Russian)
4. Koshlyakov N. S., Gliner E. B., Smirnov M. M. Partial differential equations of mathematical physics. Moscow, Vysshaia shkola Publ. (1970). (In Russian)
5. Dobrovolskis A. R. Inertia of Any Polyhedron. Icarus 124 (2), 698-704 (1996). https://doi.org/10.1006/icar.1996.0243
6. Lurie A. I. Analytical Mechanics. Moscow, Gosfizmat Publ. (1961). (In Russian)
7. Kennedy J., Eberhart R. Particle swarm optimization. Proceedings of ICNN’95 - International Conference on Neural Networks, Perth, WA, Australia 1995, 4, 1942-1948 (1995). https://doi.org/10.1109/ICNN.1995.488968
8. Poli R., Kennedy J., Blackwell T. Particle swarm optimization: an overview. Swarm Intelligence. 1, 33-57 (2007). https://doi.org/10.1007/s11721-007-0002-0
9. Nikonova E. A. Isosceles Tetrahedron and an Equimomental System of a Rigid Body. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy 10 (1), 155-164 (2023). https://doi.org/10.21638/spbu01.2023.113 (In Russian) [Eng. transl.: Vestnik St. Petersburg University. Mathematics 56 (1), 119-124 (2023). https://doi.org/10.1134/S1063454123010107].
10. Gaskell R., Jorda L., Capanna C., Hviid S., Gutierrez P. SPC SHAP5 CARTESIAN PLATE MODEL FOR COMET 67P/C-G 6K PLATES, RO-C-MULTI-5-67P-SHAPE-V2.0:CG_SPC_SHAP5_006K_CART, NASA Planetary Data System and ESA Planetary Science Archive (2017).
11. Burov A. A., Nikonov V. I. Computation of Attraction Potential of Asteroid (433) Eros with an Accuracy up to the Terms of the Fourth Order. Reports of the Russian Academy of Sciences. Physics, technical sciences 492 (1), 58-62 (2020). https://doi.org/10.31857/S2686740020030086 (In Russian) [Eng. transl.: Doklady Physics 65 (5), 164−168 (2020). https://doi.org/10.1134/S1028335820050080].
12. Burov A. A., Nikonov V. I. Sensitivity of the Euler-Poinsot Tensor Values to the Choice of the Body Surface Triangulation Mesh. Journal of Computational Mathematics and Mathematical Physics 60 (10), 1764-1776 (2020). https://doi.org/10.31857/S0044466920100063 (In Russian) [Eng. transl.: Journal of Computational Mathematics and Mathematical Physics 60 (10), 1708-1720 (2020). https://doi.org/10.1134/S0965542520100061].
13. Burov A. A., Nikonov V. I. Inertial characteristics of higher orders and dynamics in a proximity of a small celestial body. Russian Journal of Nonlinear Dynamics 16 (2), 259-273 (2020). https://doi.org/10.20537/nd200203
14. Werner R. A. The gravitational potential of a homogeneous polyhedron or don’t cut corners. Celestial Mechanics and Dynamical Astronomy 59 (3), 253-278 (1994). https://doi.org/10.1007/BF00692875
15. Werner R. A., Scheeres D. J. Exterior gravitation of a polyhedron derived and compared with harmonic and mascon gravitation representations of asteroid 4769 Castalia. Celestial Mechanics and Dynamical Astronomy 65 (3), 313-344 (1996). https://doi.org/10.1007/BF00053511
16. Franklin Ph. Equimomental systems. Studies in Applied Mathematics 8 (1-4), 129-140 (1929).
17. Sommerville D. M. Y. Equimomental tetrads of a rigid body. Math. Notes 26, 10-11 (1930). https://doi.org/10.1017/S1757748900002127
18. Talbot A. Equimomental systems. The Mathematical Gazette 36 (316), 95-110 (1952). https://doi.org/10.2307/3610326
19. Huang N. C. Equimomental system of rigidly connected equal particles. Journal of Guidance, Control, and Dynamics 16 (6), 1194-1196 (1993). https://doi.org/10.2514/3.21150
20. Gil Chica F. J., P´erez Polo M., P´erez Molina M. Note on an apparently forgotten theorem about solid rigid dynamics. European Journal of Physics 35 (4), art. 045003 (2014). https://doi.org/10.1088/0143-0807/35/4/045003
21. Chaudhary H., Saha S. K. Balancing of shaking forces and shaking moments for planar mechanisms using the equimomental systems. Mechanism and Machine Theory 43 (3), 310-334 (2008). https://doi.org/10.1016/j.mechmachtheory.2007.04.003
22. Selig J. M. Geometric Fundamentals of Robotics. 2nd ed. Berlin, Springer (2005).
23. Selig J. M. Equimomental systems and robot dynamics. IMA Mathematics of Robotics, Sept. 9-11, 2015. Oxford, St Anne’s College (2015).
24. Laus L. P., Selig J. M. Rigid body dynamics using equimomental systems of point-masses. Acta Mechanica 231, 221-236 (2020). https://doi.org/10.1007/s00707-019-02543-3
25. Nu˜nez N. N. R., Vieira R. S., Martins D. Equimomental systems representations of point-masses of planar rigid-bodies. Acta Mechanica 234, 5565-5580 (2023). https://doi.org/10.1007/s00707-023-03683-3
Downloads
Published
2024-08-10
How to Cite
Burov, A. A., Nikonova, E. A., & Nikonov, V. I. (2024). On the approximation of the field of attraction of a rigid body by the field of attraction of four material points of the same mass. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 11(2), 385–394. https://doi.org/10.21638/spbu01.2024.211
Issue
Section
Astronomy
License
Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.
