scholarly journals On Metric Invariants of Spherical Harmonics

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1470
Author(s):  
Valentin Lychagin
Keyword(s):  
Spherical Harmonics ◽  
Differential Invariants ◽  
Metric Invariants

The algebraic and differential SO3-invariants of spherical harmonics are studied in this work. The fields of rational algebraic and rational differential invariants and their applications for the description of regular SO3-orbits of spherical harmonics are given.

Zonal and tesseral harmonic perturbations of an artificial satellite

1966 ◽  
Vol 25 ◽  
pp. 323-325 ◽  
Author(s):  
B. Garfinkel
Keyword(s):  
Angular Velocity ◽  
Spherical Harmonics ◽  
Artificial Satellite ◽  
Compact Form ◽  
Earth’S Rotation ◽  
Earth's Rotation ◽  
Secular Variations ◽  
Tesseral Harmonics

The paper extends the known solution of the Main Problem to include the effects of the higher spherical harmonics of the geopotential. The von Zeipel method is used to calculate the secular variations of orderJmand the long-periodic variations of ordersJm/J2andnJm,λ/ω. HereJmandJm,λare the coefficients of the zonal and the tesseral harmonics respectively, withJm,0=Jm, andωis the angular velocity of the Earth's rotation. With the aid of the theory of spherical harmonics the results are expressed in a most compact form.

Nearly spherical vesicle shapes calculated by use of spherical harmonics : axisymmetric and nonaxisymmetric shapes and their stability

1992 ◽  
Vol 2 (5) ◽  
pp. 1081-1108 ◽  
Author(s):  
V. Heinrich ◽  
M. Brumen ◽  
R. Heinrich ◽  
S. Svetina ◽  
B. Žekš
Keyword(s):  
Spherical Harmonics ◽  
Spherical Vesicle ◽  
Vesicle Shapes

A new insight and improvement on deconvolution beamforming in spherical harmonics domain

2021 ◽  
Vol 177 ◽  
pp. 107900
Author(s):  
Zhigang Chu ◽  
Yongxin Yang ◽  
Yang Yang
Keyword(s):  
Spherical Harmonics

scholarly journals Analytical angular solutions for the atom–diatom interaction potential in a basis set of products of two spherical harmonics: two approaches

2021 ◽  
Author(s):  
Mariusz Pawlak ◽  
Marcin Stachowiak
Keyword(s):  
Spherical Harmonics ◽  
Interaction Potential ◽  
Chem Phys ◽  
Basis Set ◽  
Matrix Elements ◽  
Trigonometric Functions ◽  
Variational Theory ◽  
Molecular Collision ◽  
The Matrix ◽  
Analytical Expressions

AbstractWe present general analytical expressions for the matrix elements of the atom–diatom interaction potential, expanded in terms of Legendre polynomials, in a basis set of products of two spherical harmonics, especially significant to the recently developed adiabatic variational theory for cold molecular collision experiments [J. Chem. Phys. 143, 074114 (2015); J. Phys. Chem. A 121, 2194 (2017)]. We used two approaches in our studies. The first involves the evaluation of the integral containing trigonometric functions with arbitrary powers. The second approach is based on the theorem of addition of spherical harmonics.

On some definite integrals and a new method of reducing a function of spherical co-ordinates to a series of spherical harmonics

1903 ◽  
Vol 71 (467-476) ◽  
pp. 97-101 ◽  
Keyword(s):  
Spherical Harmonics ◽  
Fundamental Theorem ◽  
New Method ◽  
Definite Integrals

The expansion of a function f(θ) of an angle θ varying between 0 and π in terms of a series proceeding by the sines of the multiples of θ depends on the fundamental theorem, ∫ π 0 sin pθ sin qθ dθ = 0, where p and q are integer numbers not equal to each other.

HYPER-SPHERICAL HARMONICS AND ANHARMONICS IN m-DIMENSIONAL SPACE

2008 ◽  
Vol 17 (06) ◽  
pp. 1125-1130
Author(s):  
M. R. SHOJAEI ◽  
A. A. RAJABI ◽  
H. HASANABADI
Keyword(s):  
Quantum Mechanics ◽  
General Theory ◽  
Spherical Harmonics ◽  
Interaction Potential ◽  
Dimensional Space ◽  
Harmonic Polynomials ◽  
Central Importance ◽  
Computational Tools ◽  
Relative Coordinate

In quantum mechanics the hyper-spherical method is one of the most well-established and successful computational tools. The general theory of harmonic polynomials and hyper-spherical harmonics is of central importance in this paper. The interaction potential V is assumed to depend on the hyper-radius ρ only where ρ is the function of the Jacobi relative coordinate x1, x2,…, xn which are functions of the particles' relative positions.

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