oblate spheroidal coordinates

oblate spheroidal coordinates
координаты сжатого (сплющенного) сфероида,

English-russian astronautics dictionary. - M.: Military Publishing house. . 1964.

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  • Oblate spheroidal coordinates — Figure 1: Coordinate isosurfaces for a point P (shown as a black sphere) in oblate spheroidal coordinates (μ, ν, φ). The z axis is vertical, and the foci are at ±2. The red oblate spheroid (flattened sphere) corresponds to μ=1, whereas the blue… …   Wikipedia

  • Prolate spheroidal coordinates — are a three dimensional orthogonal coordinate system that results from rotating the two dimensional elliptic coordinate system about the focal axis of the ellipse, i.e., the axis on which the foci are located. Rotation about the other axis… …   Wikipedia

  • Spheroidal wave function — Spheroidal wave functions are solutions of the Laplace equation that are found by writing the equation in spheroidal coordinates and applying the technique of separation of variables, just like the use of spherical coordinates lead to spherical… …   Wikipedia

  • Oblate spheroid — An oblate spheroid An oblate spheroid is a rotationally symmetric ellipsoid having a polar axis shorter than the diameter of the equatorial circle whose plane bisects it.[1] Oblate spheroids stand in contrast to prolate spheroids. It can be… …   Wikipedia

  • Prolate spheroidal wave functions — The prolate spheroidal wave functions are a set of functions derived by timelimiting and lowpassing, and a second timelimit operation. Let Q T denote the time truncation operator, such that x=Q T x iff x is timelimited within [ T/2;T/2] .… …   Wikipedia

  • Curvilinear coordinates — Curvilinear, affine, and Cartesian coordinates in two dimensional space Curvilinear coordinates are a coordinate system for Euclidean space in which the coordinate lines may be curved. These coordinates may be derived from a set of Cartesian… …   Wikipedia

  • Orthogonal coordinates — In mathematics, orthogonal coordinates are defined as a set of d coordinates q = (q1, q2, ..., qd) in which the coordinate surfaces all meet at right angles (note: superscripts are indices, not exponents). A coordinate surface for a particular… …   Wikipedia

  • Elliptic coordinates — are a two dimensional orthogonal coordinate system in which the coordinate lines are confocal ellipses and hyperbolae. The two foci F {1} and F {2} are generally taken to be fixed at a and+a, respectively, on the x axis of the Cartesian… …   Wikipedia

  • Paraboloidal coordinates — are a three dimensional orthogonal coordinate system (λ,μ,ν) that generalizes the two dimensional parabolic coordinate system. Similar to the related ellipsoidal coordinates, the paraboloidal coordinate system has orthogonal quadratic coordinate… …   Wikipedia

  • Ellipsoidal coordinates — are a three dimensional orthogonal coordinate system (λ,μ,ν) that generalizes the two dimensional elliptic coordinate system. Unlike most three dimensional orthogonal coordinate systems that feature quadratic coordinate surfaces, the ellipsoidal… …   Wikipedia

  • Conical coordinates — Coordinate surfaces of the conical coordinates. The constants b and c were chosen as 1 and 2, respectively. The red sphere represents r=2, the blue elliptic cone aligned with the vertical z axis represents μ=cosh(1) and the yellow elliptic cone… …   Wikipedia


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