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Fix equations in docstrings of potential methods
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leouieda committed Jun 7, 2024
1 parent 894d0ae commit aa5ca21
Showing 1 changed file with 9 additions and 8 deletions.
17 changes: 9 additions & 8 deletions boule/_ellipsoid.py
Original file line number Diff line number Diff line change
Expand Up @@ -874,12 +874,13 @@ def normal_gravitational_potential(self, latitude, height):
in which :math:`V` is the gravitational potential of the
ellipsoid (no centrifugal term), :math:`GM` is the geocentric
gravitational constant, :math:`E` is the linear eccentricty,
gravitational constant, :math:`E` is the linear eccentricity,
:math:`\omega` is the angular rotation rate, :math:`q` and :math:`q_0`
are auxiliary functions, :math:`P_2` is the degree 2 unnormalized
Legendre Polynomial, and :math:`u` and :math:`beta` are ellipsoidal-
harmonic coordinates corresponding to the input geodetic latitude and
ellipsoidal height. See eq. 2-124 of [HofmannWellenhofMoritz2006]_.
Legendre Polynomial, and :math:`u` and :math:`\beta` are
ellipsoidal-harmonic coordinates corresponding to the input geodetic
latitude and ellipsoidal height. See eq. 2-124 of
[HofmannWellenhofMoritz2006]_.
Assumes that the internal density distribution of the ellipsoid is such
that the gravity potential is constant at its surface.
Expand Down Expand Up @@ -950,15 +951,15 @@ def normal_gravity_potential(self, latitude, height):
U(\beta, u) = \dfrac{GM}{E} \arctan{\dfrac{E}{u}} + \dfrac{1}{2}
\omega^2 a^2 \dfrac{q}{q_0} \left(\sin^2 \beta
- \dfrac{1}{3}\right) + \dfrac{1}{2} \omega^2 \left(u^2 + E^2)
- \dfrac{1}{3}\right) + \dfrac{1}{2} \omega^2 \left(u^2 + E^2\right)
\cos^2 \beta
in which :math:`U` is the gravity potential of the ellipsoid,
:math:`GM` is the geocentric gravitational constant, :math:`E` is the
linear eccentricty, :math:`\omega` is the angular rotation rate,
linear eccentricity, :math:`\omega` is the angular rotation rate,
:math:`q` and :math:`q_0` are auxiliary functions, and :math:`u` and
:math:`beta` are ellipsoidal-harmonic coordinates corresponding to the
input geodetic latitude and and ellipsoidal height. See eq. 2-126 of
:math:`\beta` are ellipsoidal-harmonic coordinates corresponding to the
input geodetic latitude and ellipsoidal height. See eq. 2-126 of
[HofmannWellenhofMoritz2006]_.
Assumes that the internal density distribution of the ellipsoid is such
Expand Down

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