×

zbMATH — the first resource for mathematics

Sensitivity of the Euler-Poinsot tensor values to the choice of the body surface triangulation mesh. (English. Russian original) Zbl 1454.85003
Comput. Math. Math. Phys. 60, No. 10, 1708-1720 (2020); translation from Zh. Vychisl. Mat. Mat. Fiz. 60, No. 10, 1764-1776 (2020).
Summary: The inertial characteristics of celestial bodies can be calculated using their triangle partitions based on photometric observations. Such partitions can be refined along with the accumulation of necessary information. In this regard, the question arises to what extent the approximations of the inertial characteristics of celestial bodies, in particular, the approximations of the components of the Euler-Poinsot tensor of different orders, are susceptible to the choice of such partitions. Such components enter into the expansion of the gravitational potential in harmonic polynomials. In this paper, for some small celestial bodies, a comparison of such coefficients is carried out as coarse partitions are replaced with finer ones.
MSC:
85A15 Galactic and stellar structure
85-08 Computational methods for problems pertaining to astronomy and astrophysics
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Appell, P., Leçons sur l’attraction et la fonction potentielle: professées à la Sorbonne en 1890-1891 (1892), Paris: G. Carrie, Paris · JFM 24.0924.02
[2] H. Poincaré, Théorie du potentiel newtonien: Leçons professées à la Sorbonne pendant le premier semestre 1894-1895 (Gauthier-Villars, Paris, 1899). · JFM 30.0692.01
[3] Duboshin, G. N., Theory of Gravitation (1961), Moscow: Fizmatlit, Moscow · Zbl 0102.39201
[4] Sretenskii, L. N., Theory of Newtonian Potentials (1946), Moscow: Gostekhizdat, Moscow
[5] V. V. Beletskii, Motion of an Artificial Satellite about Its Center of Mass (Nauka, Moscow, 1965; Israel Program for Scientific Translations, 1966). · Zbl 0138.20301
[6] G. N. Duboshin, Celestial Mechanics: Basic Problems and Methods (Fizmatlit, Moscow, 1968; Defense Tech. Inf. Center, Fort Belvoir, 1969). · Zbl 0199.59903
[7] Antonov, V. A.; Timoshkova, E. I.; Kholshevnikov, K. V., Introduction to the Theory of Newtonian Potentials (1988), Moscow: Fizmatlit, Moscow · Zbl 0677.31001
[8] Doubochine, G. N., Sur le développement de la fonction des forces dans le problème de deux corps finis, Celestial Mech., 14, 239-281 (1976) · Zbl 0346.70007
[9] Dobrovolskis, A. R., Inertia of any polyhedron, Icarus, 124, 698-704 (1996)
[10] Mirtich, B., Fast and accurate computation of polyhedral mass properties, J. Graphics Tools, 1, 31-50 (1996)
[11] F. A. Sludskii, Master’s Dissertation in Astronomy (Universitetskaya (Katkov K), Moscow, 1863).
[12] Werner, R. A., The gravitational potential of a homogeneous polyhedron or don’t cut corners, Celestial Mech. Dyn. Astron., 59, 253-278 (1994) · Zbl 0825.70059
[13] 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 Mech. Dyn. Astron., 65, 313-344 (1996) · Zbl 0881.70008
[14] 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, Dokl. Phys., 65, 164-168 (2020)
[15] Nikonov, V. I., Gravitational Fields of Small Celestial Bodies (2020), Moscow: Belyi Veter, Moscow
[16] Burov, A. A.; Nikonov, V. I., Inertial characteristics of higher orders and dynamics in a proximity of a small celestial body, Russ. J. Nonlinear Dyn., 16, 259-273 (2020) · Zbl 1459.70033
[17] Werner, R. A., Spherical harmonic coefficients for the potential of a constant-density polyhedron, Comput. Geosci., 23, 1071-1077 (1997)
[18] D. Liao-McPherson, W. D. Dunham, and I. Kolmanovsky, “Model predictive control strategies for constrained soft landing on an asteroid,” AIAA/AAS Astrodynamics Specialist Conference, September 13-16, 2016, Long Beach, California (2016).
[19] Thomas, P. C.; Joseph, J.; Carcich, B., Eros: Shape, topography, and slope processes, Icarus, 155, 18-37 (2002)
[20] Zuber, M. T.; Smith, D. E.; Cheng, A. F., The shape of 433 Eros from the NEAR-Shoemaker laser rangefinder, Science, 289, 2097-2100 (2000)
[21] Miller, J. K.; Konopliv, A. S.; Antreasian, P. G., Determination of shape, gravity, and rotational state of asteroid 433 Eros, Icarus, 155, 3-17 (2002)
[22] Farnham, T. L., Shape model of asteroid 21 Lutetia, RO-A-OSINAC/OSIWAC-5-LUTETIA-SHAPE-V1.0 (2013)
[23] C. Capanna, L. Jorda, P. Gutierrez, and S. Hviid, “MSPCD SHAP2 Cartesian plate model for comet 67P/C-G 6K PLATES, RO-C-MULTI-5-67P-SHAPE-V1.0:CG_MSPCD_SHAP2_006K_CART” (NASA Planetary Data System and ESA Planetary Science Archive, 2015).
[24] C. Capanna, L. Jorda, P. Gutierrez, and S. Hviid, “MSPCD SHAP2 Cartesian plate model for comet 67P/C-G 12K PLATES, RO-C-MULTI-5-67P-SHAPE-V1.0:CG_MSPCD_SHAP2_012K_CART” (NASA Planetary Data System and ESA Planetary Science Archive, 2015).
[25] C. Capanna, L. Jorda, P. Gutierrez, and S. Hviid, “MSPCD SHAP2 Cartesian plate model for comet 67P/C-G 24K PLATES, RO-C-MULTI-5-67P-SHAPE-V1.0:CG_MSPCD_SHAP2_024K_CART” (NASA Planetary Data System and ESA Planetary Science Archive, 2015).
[26] C. Capanna, L. Jorda, P. Gutierrez, and S. Hviid, “MSPCD SHAP2 Cartesian plate model for comet 67P/C-G 48K PLATES, RO-C-MULTI-5-67P-SHAPE-V1.0:CG_MSPCD_SHAP2_048K_CART” (NASA Planetary Data System and ESA Planetary Science Archive, 2015).
[27] C. Capanna, L. Jorda, P. Gutierrez, and S. Hviid, “MSPCD SHAP2 Cartesian plate model for comet 67P/C-G 98K PLATES, RO-C-MULTI-5-67P-SHAPE-V1.0:CG_MSPCD_SHAP2_098K_CART” (NASA Planetary Data System and ESA Planetary Science Archive, 2015).
[28] Wang, X.; Jiang, Y.; Gong, Sh., Analysis of the potential field and equilibrium points of irregular-shaped minor celestial bodies, Astrophys. Space Sci., 353, 105-121 (2014)
[29] Jiang, Y.; Baoyin, H.; Li, H., Collision and annihilation of relative equilibrium points around asteroids with a changing parameter, Mon. Not. R. Astron. Soc., 452, 3924-3931 (2015)
[30] Jiang, Y.; Baoyin, H., Annihilation of relative equilibria in the gravitational field of irregular-shaped minor celestial bodies, Planet. Space Sci., 161, 107-136 (2018)
[31] Aljbaae, S.; Chanut, T. G. G.; Carruba, V., The dynamical environment of asteroid 21 Lutetia according to different internal models, Mon. Not. R. Astron. Soc., 464, 3552-3560 (2017)
[32] Werner, R. A., The solid angle hidden in polyhedron gravitation formulations, J. Geodesy, 91, 307-328 (2017)
[33] Markeev, A. P., Libration Points in Celestial Mechanics and Astrodynamics (1978), Moscow: Fizmatlit, Moscow
[34] Abalakin, V. K., On the stability of libration points of a rotating gravitating ellipsoid, Byull. Inst. Teor. Astron., 6, 543-549 (1957)
[35] Batrakov, Yu. V., Periodic motion of a particle in the gravitational field of a rotating triaxial ellipsoid, Byull. Inst. Teor. Astron., 6, 524-542 (1957)
[36] S. G. Zhuravlev, “Instability of libration points of a rotating gravitating ellipsoid,” in Collected Research Papers of Postgraduate Students (Univ. Druzhby Narodov, Moscow, 1968), No. 1, pp. 169-183 [in Russian].
[37] Zhuravlev, S. G., Stability of the libration points of a rotating triaxial ellipsoid, Celestial Mech., 6, 255-267 (1972) · Zbl 0254.70007
[38] Zhuravlev, S. G., About the stability of the libration points of a rotating triaxial ellipsoid in a degenerate case, Celestial Mech., 8, 75-84 (1973) · Zbl 0276.70011
[39] Zhuravlev, S. G., Stability of the libration points of a rotating triaxial ellipsoid in the three-dimensional case, Astron. Zh., 51, 1330-1334 (1974) · Zbl 0288.70007
[40] Kosenko, I. I., On libration points near a gravitating and rotating triaxial ellipsoid, J. Appl. Math. Mech., 45, 18-23 (1981) · Zbl 0486.70013
[41] Kosenko, I. I., Libration points in the problem of a triaxial gravitating ellipsoid: Geometry of the stability domain, Kosm. Issled., 19, 200-209 (1981)
[42] Kosenko, I. I., Nonlinear analysis of the stability of the libration points of a triaxial ellipsoid, J. Appl. Math. Mech., 49, 17-24 (1985) · Zbl 0598.70014
[43] Kosenko, I. I., On a power series expansion of the gravitational potential of an inhomogeneous ellipsoid, J. Appl. Math. Mech., 50, 142-146 (1986) · Zbl 0619.70003
[44] Kosenko, I. I., On the stability of points of libration of an inhomogeneous triaxial ellipsoid, J. Appl. Math. Mech., 51, 1-5 (1987) · Zbl 0653.70009
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.