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Generating function of the inertial integrals for small celestial bodiesстатья
- Авторы: Burov Alexander A., Nikonova Ekaterina A.
- Журнал: Celestial Mechanics and Dynamical Astronomy
- Том: 134
- Номер: 4
- Год издания: 2022
- Издательство: Springer Nature
- Местоположение издательства: Switzerland
- Номер статьи: 37
- DOI: 10.1007/s10569-022-10087-3
- Аннотация: The properties of generating functions used to calculate inertial integrals are discussed, and examples are given of their use in calculating such integrals for various small celestial bodies. The introduction describes the objectives of the research and also gives a brief overview of the works devoted to the history of the use of inertial integrals. The problem statement is formulated, the results obtained earlier are summarized, and a theorem on the behavior of inertia integrals under translation, rotation, and dilation is given. For an arbitrary homogeneous tetrahedron, the generating functions are written out explicitly. The possibility of obtaining the same expressions for inertia integrals based on the classical theorem introduced by Lejeune Dirichlet is discussed. The generating functions written out in this way for the tetrahedron are used to calculate inertia integrals for such small celestial bodies as asteroids (532) Herculina, (321) Florentina, (16) Psyche, (45) Eugenia, and (101955) Bennu, whose surfaces are approximated by polyhedra. There are two appendixes. Appendix A recalls thegeneral view of the expansion of the potential over a small parameter with inertial integrals as coefficients. The connection of inertial integrals with Stokes coefficients, widely used in celestial mechanics, is described. Definitions of generating functions for massive objects with fewer than three dimensions are given in Appendix B. Such functions are written out for a system of material points, for a homogeneous straight segment, and for a homogeneoustriangular lamina. An isosceles tetrahedron is considered as an illustrative example. The cases when its mass is concentrated (a) at the vertices, (b) on the edges, and (c) on the facets are considered. Generating functions and inertial integrals up to the fourth order are written out and compared for these cases.
- Добавил в систему: Никонова Екатерина Александровна