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1: 28.32 Mathematical Applications
§28.32(i) Elliptical Coordinates and an Integral Relationship
If the boundary conditions in a physical problem relate to the perimeter of an ellipse, then elliptical coordinates are convenient. …
2: 31.17 Physical Applications
Introduce elliptic coordinates z 1 and z 2 on S 2 . Then …
3: 28.33 Physical Applications
  • Boundary-values problems arising from solution of the two-dimensional wave equation in elliptical coordinates. This yields a pair of equations of the form (28.2.1) and (28.20.1), and the appropriate solution of (28.2.1) is usually a periodic solution of integer order. See §28.33(ii).

  • Physical problems involving Mathieu functions include vibrational problems in elliptical coordinates; see (28.32.1). …In elliptical coordinates (28.32.2) becomes (28.32.3). …
    4: 23.21 Physical Applications
    §23.21(iii) Ellipsoidal Coordinates
    5: 23.20 Mathematical Applications
    23.20.2 C : y 2 z = x 3 + a x z 2 + b z 3 ,
    6: 29.18 Mathematical Applications
    29.18.6 d 2 u 2 d β 2 + ( h - ν ( ν + 1 ) k 2 sn 2 ( β , k ) ) u 2 = 0 ,
    29.18.7 d 2 u 3 d γ 2 + ( h - ν ( ν + 1 ) k 2 sn 2 ( γ , k ) ) u 3 = 0 ,
    7: 22.19 Physical Applications
    22.19.6 x ( t ) = a cn ( t 1 + 2 η , k ) .
    22.19.7 x ( t ) = a sn ( t 1 - η , k ) .
    22.19.9 x ( t ) = a cn ( t 2 η - 1 , k ) ,
    8: 22.18 Mathematical Applications
    §22.18 Mathematical Applications
    §22.18(i) Lengths and Parametrization of Plane Curves
    §22.18(iv) Elliptic Curves and the Jacobi–Abel Addition Theorem
    9: 36.5 Stokes Sets
    For z 0 , the Stokes set is expressed in terms of scaled coordinates
    §36.5(iii) Umbilics
    Elliptic Umbilic Stokes Set (Codimension three)
    With coordinates
    See accompanying text
    Figure 36.5.5: Elliptic umbilic catastrophe with z = constant . … Magnify
    10: Bibliography P
  • F. A. Paxton and J. E. Rollin (1959) Tables of the Incomplete Elliptic Integrals of the First and Third Kind. Technical report Curtiss-Wright Corp., Research Division, Quehanna, PA.
  • S. Pratt (2007) Comoving coordinate system for relativistic hydrodynamics. Phy. Rev. C 75, pp. (024907–1)–(024907–10).
  • W. H. Press and S. A. Teukolsky (1990) Elliptic integrals. Computers in Physics 4 (1), pp. 92–96.