Transformation of Irregular Solid Spherical Harmonics with Parallel Translation of the Coordinate System
- Авторлар: Aganin A.1, Davletshin A.1
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Мекемелер:
- Institute of Mechanics and Engineering, Kazan Scientific Center
- Шығарылым: Том 39, № 3 (2018)
- Беттер: 433-438
- Бөлім: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/201893
- DOI: https://doi.org/10.1134/S1995080218030022
- ID: 201893
Дәйексөз келтіру
Аннотация
Solid spherical harmonics and spherical functions are widely used for studying physical phenomena in spatial domains bounded by spherical or nearly-spherical surfaces. In this case, it is frequently needed to transform these functions with a parallel translation of the coordinate system. Specifically, this scenario arises in describing the hydrodynamic interaction of spherical or weakly-nonspherical gas bubbles in the unbounded volume of an incompressible fluid. In the two-dimensional (axisymmetric) case, when Legendre polynomials act as spherical functions, the transformation can be conducted with a well-known compact expression. In the three-dimensional case, similar well-known expressions are rather complex (for example, the Clebsch–Gordan coefficients are used in these expressions), which makes their use difficult. This paper describes a derivation of such an expression that naturally leads to a compact form of the respective coefficients. Actually, these coefficients are a generalization to the three-dimensional case of similar well-known coefficients in the two-dimensional (axisymmetric) case.
Негізгі сөздер
Авторлар туралы
A. Aganin
Institute of Mechanics and Engineering, Kazan Scientific Center
Хат алмасуға жауапты Автор.
Email: aganin@kfti.knc.ru
Ресей, Kazan, 420111
A. Davletshin
Institute of Mechanics and Engineering, Kazan Scientific Center
Email: aganin@kfti.knc.ru
Ресей, Kazan, 420111