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#pragma once
/**
* \file NETGeographicLib/NormalGravity.h
* \brief Header for NETGeographicLib::NormalGravity class
*
* NETGeographicLib is copyright (c) Scott Heiman (2013)
* GeographicLib is Copyright (c) Charles Karney (2010-2012)
* <charles@karney.com> and licensed under the MIT/X11 License.
* For more information, see
* http://geographiclib.sourceforge.net/
**********************************************************************/
namespace NETGeographicLib
{
ref class Geocentric;
/**
* \brief .NET wrapper for GeographicLib::NormalGravity.
*
* This class allows .NET applications to access GeographicLib::NormalGravity.
*
* "Normal" gravity refers to an idealization of the earth which is modeled
* as an rotating ellipsoid. The eccentricity of the ellipsoid, the rotation
* speed, and the distribution of mass within the ellipsoid are such that the
* surface of the ellipsoid is a surface of constant potential (gravitational
* plus centrifugal). The acceleration due to gravity is therefore
* perpendicular to the surface of the ellipsoid.
*
* There is a closed solution to this problem which is implemented here.
* Series "approximations" are only used to evaluate certain combinations of
* elementary functions where use of the closed expression results in a loss
* of accuracy for small arguments due to cancellation of the two leading
* terms. However these series include sufficient terms to give full machine
* precision.
*
* Definitions:
* - <i>V</i><sub>0</sub>, the gravitational contribution to the normal
* potential;
* - Φ, the rotational contribution to the normal potential;
* - \e U = <i>V</i><sub>0</sub> + Φ, the total
* potential;
* - <b>Γ</b> = ∇<i>V</i><sub>0</sub>, the acceleration due to
* mass of the earth;
* - <b>f</b> = ∇Φ, the centrifugal acceleration;
* - <b>γ</b> = ∇\e U = <b>Γ</b> + <b>f</b>, the normal
* acceleration;
* - \e X, \e Y, \e Z, geocentric coordinates;
* - \e x, \e y, \e z, local cartesian coordinates used to denote the east,
* north and up directions.
*
* References:
* - W. A. Heiskanen and H. Moritz, Physical Geodesy (Freeman, San
* Francisco, 1967), Secs. 1-19, 2-7, 2-8 (2-9, 2-10), 6-2 (6-3).
* - H. Moritz, Geodetic Reference System 1980, J. Geodesy 54(3), 395-405
* (1980) http://dx.doi.org/10.1007/BF02521480
*
* C# Example:
* \include example-NormalGravity.cs
* Managed C++ Example:
* \include example-NormalGravity.cpp
* Visual Basic Example:
* \include example-NormalGravity.vb
*
* <B>INTERFACE DIFFERENCES:</B><BR>
* A constructor has been provided for creating standard WGS84 and GRS80
* gravity models.
*
* The following functions are implemented as properties:
* MajorRadius, MassConstant, AngularVelocity, Flattening,
* EquatorialGravity, PolarGravity, GravityFlattening, SurfacePotential.
**********************************************************************/
public ref class NormalGravity
{
private:
// a pointer to the unmanaged GeographicLib::NormalGravity.
const GeographicLib::NormalGravity* m_pNormalGravity;
// the finalizer frees the unmanaged memory when the object is destroyed.
!NormalGravity(void);
public:
/// \cond SKIP
//! The enumerated standard gravity models.
enum class StandardModels
{
WGS84, //!< WGS84 gravity model.
GRS80 //!< GRS80 gravity model.
};
/// \endcond
/** \name Setting up the normal gravity
**********************************************************************/
///@{
/**
* Constructor for the normal gravity.
*
* @param[in] a equatorial radius (meters).
* @param[in] GM mass constant of the ellipsoid
* (meters<sup>3</sup>/seconds<sup>2</sup>); this is the product of \e G
* the gravitational constant and \e M the mass of the earth (usually
* including the mass of the earth's atmosphere).
* @param[in] omega the angular velocity (rad s<sup>−1</sup>).
* @param[in] f the flattening of the ellipsoid.
* @param[in] J2 dynamical form factor.
* @exception if \e a is not positive or the other constants are
* inconsistent (see below).
*
* Exactly one of \e f and \e J2 should be positive and this will be used
* to define the ellipsoid. The shape of the ellipsoid can be given in one
* of two ways:
* - geometrically, the ellipsoid is defined by the flattening \e f = (\e a
* − \e b) / \e a, where \e a and \e b are the equatorial radius
* and the polar semi-axis.
* - physically, the ellipsoid is defined by the dynamical form factor
* <i>J</i><sub>2</sub> = (\e C − \e A) / <i>Ma</i><sup>2</sup>,
* where \e A and \e C are the equatorial and polar moments of inertia
* and \e M is the mass of the earth.
**********************************************************************/
NormalGravity(double a, double GM, double omega, double f, double J2);
/**
* A constructor for creating standard gravity models..
* @param[in] model Specifies the desired model.
**********************************************************************/
NormalGravity(StandardModels model);
/**
* A constructor that accepts a GeographicLib::NormalGravity.
* For internal use only.
* @param g An existing GeographicLib::NormalGravity.
**********************************************************************/
NormalGravity( const GeographicLib::NormalGravity& g);
///@}
/**
* The destructor calls the finalizer.
**********************************************************************/
~NormalGravity()
{ this->!NormalGravity(); }
/** \name Compute the gravity
**********************************************************************/
///@{
/**
* Evaluate the gravity on the surface of the ellipsoid.
*
* @param[in] lat the geographic latitude (degrees).
* @return γ the acceleration due to gravity, positive downwards
* (m s<sup>−2</sup>).
*
* Due to the axial symmetry of the ellipsoid, the result is independent of
* the value of the longitude. This acceleration is perpendicular to the
* surface of the ellipsoid. It includes the effects of the earth's
* rotation.
**********************************************************************/
double SurfaceGravity(double lat);
/**
* Evaluate the gravity at an arbitrary point above (or below) the
* ellipsoid.
*
* @param[in] lat the geographic latitude (degrees).
* @param[in] h the height above the ellipsoid (meters).
* @param[out] gammay the northerly component of the acceleration
* (m s<sup>−2</sup>).
* @param[out] gammaz the upward component of the acceleration
* (m s<sup>−2</sup>); this is usually negative.
* @return \e U the corresponding normal potential.
*
* Due to the axial symmetry of the ellipsoid, the result is independent of
* the value of the longitude and the easterly component of the
* acceleration vanishes, \e gammax = 0. The function includes the effects
* of the earth's rotation. When \e h = 0, this function gives \e gammay =
* 0 and the returned value matches that of NormalGravity::SurfaceGravity.
**********************************************************************/
double Gravity(double lat, double h,
[System::Runtime::InteropServices::Out] double% gammay,
[System::Runtime::InteropServices::Out] double% gammaz);
/**
* Evaluate the components of the acceleration due to gravity and the
* centrifugal acceleration in geocentric coordinates.
*
* @param[in] X geocentric coordinate of point (meters).
* @param[in] Y geocentric coordinate of point (meters).
* @param[in] Z geocentric coordinate of point (meters).
* @param[out] gammaX the \e X component of the acceleration
* (m s<sup>−2</sup>).
* @param[out] gammaY the \e Y component of the acceleration
* (m s<sup>−2</sup>).
* @param[out] gammaZ the \e Z component of the acceleration
* (m s<sup>−2</sup>).
* @return \e U = <i>V</i><sub>0</sub> + Φ the sum of the
* gravitational and centrifugal potentials
* (m<sup>2</sup> s<sup>−2</sup>).
*
* The acceleration given by <b>γ</b> = ∇\e U =
* ∇<i>V</i><sub>0</sub> + ∇Φ = <b>Γ</b> + <b>f</b>.
**********************************************************************/
double U(double X, double Y, double Z,
[System::Runtime::InteropServices::Out] double% gammaX,
[System::Runtime::InteropServices::Out] double% gammaY,
[System::Runtime::InteropServices::Out] double% gammaZ);
/**
* Evaluate the components of the acceleration due to gravity alone in
* geocentric coordinates.
*
* @param[in] X geocentric coordinate of point (meters).
* @param[in] Y geocentric coordinate of point (meters).
* @param[in] Z geocentric coordinate of point (meters).
* @param[out] GammaX the \e X component of the acceleration due to gravity
* (m s<sup>−2</sup>).
* @param[out] GammaY the \e Y component of the acceleration due to gravity
* (m s<sup>−2</sup>).
* @param[out] GammaZ the \e Z component of the acceleration due to gravity
* (m s<sup>−2</sup>).
* @return <i>V</i><sub>0</sub> the gravitational potential
* (m<sup>2</sup> s<sup>−2</sup>).
*
* This function excludes the centrifugal acceleration and is appropriate
* to use for space applications. In terrestrial applications, the
* function NormalGravity::U (which includes this effect) should usually be
* used.
**********************************************************************/
double V0(double X, double Y, double Z,
[System::Runtime::InteropServices::Out] double% GammaX,
[System::Runtime::InteropServices::Out] double% GammaY,
[System::Runtime::InteropServices::Out] double% GammaZ);
/**
* Evaluate the centrifugal acceleration in geocentric coordinates.
*
* @param[in] X geocentric coordinate of point (meters).
* @param[in] Y geocentric coordinate of point (meters).
* @param[out] fX the \e X component of the centrifugal acceleration
* (m s<sup>−2</sup>).
* @param[out] fY the \e Y component of the centrifugal acceleration
* (m s<sup>−2</sup>).
* @return Φ the centrifugal potential (m<sup>2</sup>
* s<sup>−2</sup>).
*
* Φ is independent of \e Z, thus \e fZ = 0. This function
* NormalGravity::U sums the results of NormalGravity::V0 and
* NormalGravity::Phi.
**********************************************************************/
double Phi(double X, double Y,
[System::Runtime::InteropServices::Out] double% fX,
[System::Runtime::InteropServices::Out] double% fY);
///@}
/** \name Inspector functions
**********************************************************************/
///@{
/**
* @return \e a the equatorial radius of the ellipsoid (meters). This is
* the value used in the constructor.
**********************************************************************/
property double MajorRadius { double get(); }
/**
* @return \e GM the mass constant of the ellipsoid
* (m<sup>3</sup> s<sup>−2</sup>). This is the value used in the
* constructor.
**********************************************************************/
property double MassConstant { double get(); }
/**
* @return \e J<sub>n</sub> the dynamical form factors of the ellipsoid.
*
* If \e n = 2 (the default), this is the value of <i>J</i><sub>2</sub>
* used in the constructor. Otherwise it is the zonal coefficient of the
* Legendre harmonic sum of the normal gravitational potential. Note that
* \e J<sub>n</sub> = 0 if \e n is odd. In most gravity applications,
* fully normalized Legendre functions are used and the corresponding
* coefficient is <i>C</i><sub><i>n</i>0</sub> = −\e J<sub>n</sub> /
* sqrt(2 \e n + 1).
**********************************************************************/
double DynamicalFormFactor(int n);
/**
* @return ω the angular velocity of the ellipsoid (rad
* s<sup>−1</sup>). This is the value used in the constructor.
**********************************************************************/
property double AngularVelocity { double get(); }
/**
* @return <i>f</i> the flattening of the ellipsoid (\e a − \e b)/\e
* a.
**********************************************************************/
property double Flattening { double get(); }
/**
* @return γ<sub>e</sub> the normal gravity at equator (m
* s<sup>−2</sup>).
**********************************************************************/
property double EquatorialGravity { double get(); }
/**
* @return γ<sub>p</sub> the normal gravity at poles (m
* s<sup>−2</sup>).
**********************************************************************/
property double PolarGravity { double get(); }
/**
* @return <i>f*</i> the gravity flattening (γ<sub>p</sub> −
* γ<sub>e</sub>) / γ<sub>e</sub>.
**********************************************************************/
property double GravityFlattening { double get(); }
/**
* @return <i>U</i><sub>0</sub> the constant normal potential for the
* surface of the ellipsoid (m<sup>2</sup> s<sup>−2</sup>).
**********************************************************************/
property double SurfacePotential { double get(); }
/**
* @return the Geocentric object used by this instance.
**********************************************************************/
Geocentric^ Earth();
///@}
/**
* A global instantiation of NormalGravity for the WGS84 ellipsoid.
**********************************************************************/
static NormalGravity^ WGS84();
/**
* A global instantiation of NormalGravity for the GRS80 ellipsoid.
**********************************************************************/
static NormalGravity^ GRS80();
/**
* Compute the flattening from the dynamical form factor.
*
* @param[in] a equatorial radius (meters).
* @param[in] GM mass constant of the ellipsoid
* (meters<sup>3</sup>/seconds<sup>2</sup>); this is the product of \e G
* the gravitational constant and \e M the mass of the earth (usually
* including the mass of the earth's atmosphere).
* @param[in] omega the angular velocity (rad s<sup>−1</sup>).
* @param[in] J2 the dynamical form factor.
* @return \e f the flattening of the ellipsoid.
**********************************************************************/
static double J2ToFlattening(double a, double GM, double omega,
double J2);
/**
* Compute the dynamical form factor from the flattening.
*
* @param[in] a equatorial radius (meters).
* @param[in] GM mass constant of the ellipsoid
* (meters<sup>3</sup>/seconds<sup>2</sup>); this is the product of \e G
* the gravitational constant and \e M the mass of the earth (usually
* including the mass of the earth's atmosphere).
* @param[in] omega the angular velocity (rad s<sup>−1</sup>).
* @param[in] f the flattening of the ellipsoid.
* @return \e J2 the dynamical form factor.
**********************************************************************/
static double FlatteningToJ2(double a, double GM, double omega,
double f);
};
} //namespace NETGeographicLib
|
