Elliptic coordinate system

About: Elliptic coordinate system is a research topic. Over the lifetime, 670 publications have been published within this topic receiving 11135 citations. The topic is also known as: elliptical coordinate system & elliptic coordinates.

Multipole structure and coordinate systems

Abstract: Multipole expansions depend on the coordinate system, so that coefficients of multipole moments can be set equal to zero by an appropriate choice of coordinates. Therefore, it is meaningless to say that a physical system has a nonvanishing quadrupole moment, say, without specifying which coordinate system is used. (Except if this moment is the lowest non-vanishing one.) This result is demonstrated for the case of two equal like electric charges. Specifically, an adapted coordinate system in which the potential is given by a monopole term only is explicitly found, the coefficients of all higher multipoles vanish identically. It is suggested that this result can be generalized to other potential problems, by making equal coordinate surfaces adapt to the potential problem's equipotential surfaces.

Calculation of the Streaming Potential Near a Rotating Disk with Rotational Elliptic Coordinates

Abstract: The calculation with rotational elliptic coordinates of the streaming potential in the vicinity of a disk-shaped sample rotating in an electrolytic solution is presented. The measurement of this streaming potential is used to determine the zeta potential of planar surfaces. Rotational elliptic coordinates are favored in relation to integral transform methods because only simple mathematical methods are employed to explain the theory of this technique.

Interaction of a submerged elliptic plate with waves

Abstract: With potential applications as a breakwater, an elliptic plate horizontally submerged in waves is investigated within the scope of linear wave theory. An elliptical coordinate system is adopted, which has an advantage to represent the solution in an analytical form, i.e. an expansion of eigen functions. By means of separation of variables, it turns out that the eigen functions in the elliptical coordinates consist of the Mathieu functions and the modified Mathieu functions. The interaction of the elliptic plate with the waves is studied. The wave loads, as well as the scattered wave field, are evaluated.

Separation of variables in Einstein spaces. II. No ignorable coordinates

Abstract: We prove that the only Einstein spaces which admit a coordinate system with no ignorable coordinates which separates the Hamilton-Jacobi equation are certain symmetric spaces of Petrov typeD due to Kasner and the constant-curvature de Sitter spaces. We also show that a space admitting a coordinate system with no ignorable coordinates which separates the Helmholtz (Schrodinger) equation must be of Petrov type

T 3 deformations and β-deformed geometries

Abstract: We discuss $\ensuremath{\beta}$-deformed geometries on two types of ${T}^{3}$'s where the direction along the third coordinate is not orthogonal to the direction along the second coordinate or the direction along the first coordinate. We show that the intersection angle between the direction along the third coordinate and the direction along the second coordinate corresponds to the parameter of the S-duality of the $\ensuremath{\beta}$-deformation, while the intersection angle between the direction along the third coordinate and the direction along the first coordinate generalizes the $\ensuremath{\beta}$-deformed geometry.