"Variational methods in the representation of the gravitational potential"@en . . "632756" . "RIV/00025615:_____/03:00007362!RIV/2004/MSM/C01004/N" . "Earth's gravity field;boundary value problems;variational methods;ellipsoidal harmonics"@en . "9"^^ . . . "2001-10-23+02:00"^^ . "1"^^ . . . . . "Luxembourg" . "RIV/00025615:_____/03:00007362" . . "[7DE79B7ACD33]" . "1"^^ . . . "Centre Europ\u00E9en de G\u00E9odynamique et de S\u00E9ismologie" . "Variational methods in the representation of the gravitational potential"@en . "Muensbach" . "Variational methods in the representation of the gravitational potential" . . . . "Variational methods in the representation of the gravitational potential" . "Holota, Petr" . . "P(GA205/01/1463), P(LA 089), P(LN00A005)" . . . "Cahiers du Centre Europ\u00E9en de G\u00E9odynamique et de S\u00E9ismologie" . "The determination of the gravity field of the Earth is approached from the mathematical point of view. We discuss the integration of Laplace's equation under given boundary data. In particular we focus on the solution of a gravimetric boundary value problem. An approach is applied that follows the concept of variational methods and the notion of the weak solution. A system of elementary potentials is used as a function basis. We then construct Galerkin's system of linear equations for the coefficients in the approximation of the disturbing potential by means of linear combinations of basis functions. Elements of the matrix of this system are computed for the exterior of an ellipsoid of revolution. Ellipsoidal harmonics are used as a natural tool in these computations. The effects caused by the flattening of the ellipsoid are expressed up to terms multiplied by the square of the numerical eccentricity. A reference is also made which concerns effects caused by the topography." . "2-9599804-9-2" . . "The determination of the gravity field of the Earth is approached from the mathematical point of view. We discuss the integration of Laplace's equation under given boundary data. In particular we focus on the solution of a gravimetric boundary value problem. An approach is applied that follows the concept of variational methods and the notion of the weak solution. A system of elementary potentials is used as a function basis. We then construct Galerkin's system of linear equations for the coefficients in the approximation of the disturbing potential by means of linear combinations of basis functions. Elements of the matrix of this system are computed for the exterior of an ellipsoid of revolution. Ellipsoidal harmonics are used as a natural tool in these computations. The effects caused by the flattening of the ellipsoid are expressed up to terms multiplied by the square of the numerical eccentricity. A reference is also made which concerns effects caused by the topography."@en . . "3-11" . .