The derivation of conservation laws for the wave equation on sphere, cone and flat space is considered. The partial Noether approach is applied for wave equation on curved surfaces in terms of the coefficients of the ...The derivation of conservation laws for the wave equation on sphere, cone and flat space is considered. The partial Noether approach is applied for wave equation on curved surfaces in terms of the coefficients of the first fundamental form （FFF） and the partial Noether operator＇s determining equations are derived. These determining equations are then used to construct the partial Noether operators and conserved vectors for the wave equation on different surfaces. The conserved vectors for the wave equation on the sphere, cone and fiat space are simplified using the Lie point symmetry generators of the equation and conserved vectors with the help of the symmetry conservation laws relation.展开更多
A new form of geodetic coordinate system based on geodesic coordinates instead of geodetic longitude and latitude was proposed.The vertical and horizontal geodesic coordinates measured with length were defined as coor...A new form of geodetic coordinate system based on geodesic coordinates instead of geodetic longitude and latitude was proposed.The vertical and horizontal geodesic coordinates measured with length were defined as coordinate parameters,but the two families of coordinate curves were still meridians and parallel circles.The first fundamental form on the ellipsoidal surface and its three coefficients were deduced by the geodesic coordinate.The formula for the latitudinal scale factor of length for geodetic parallel lines was derived,by which the obtained result conformed to that standard value calculated from geodetic latitude,and it is applicable in the range of 400 km from north to south.Therefore,it lays the foundation for establishing the differential equation and differential relationship based on this type of coordinate parameters;and consequently,it is convenient and accurate enough to operate on the ellipsoidal surface in this new form of geodetic coordinate system.展开更多
文摘The derivation of conservation laws for the wave equation on sphere, cone and flat space is considered. The partial Noether approach is applied for wave equation on curved surfaces in terms of the coefficients of the first fundamental form （FFF） and the partial Noether operator＇s determining equations are derived. These determining equations are then used to construct the partial Noether operators and conserved vectors for the wave equation on different surfaces. The conserved vectors for the wave equation on the sphere, cone and fiat space are simplified using the Lie point symmetry generators of the equation and conserved vectors with the help of the symmetry conservation laws relation.
基金supported by the National Natural Science Foundation of China(Grant No.40471114).
文摘A new form of geodetic coordinate system based on geodesic coordinates instead of geodetic longitude and latitude was proposed.The vertical and horizontal geodesic coordinates measured with length were defined as coordinate parameters,but the two families of coordinate curves were still meridians and parallel circles.The first fundamental form on the ellipsoidal surface and its three coefficients were deduced by the geodesic coordinate.The formula for the latitudinal scale factor of length for geodetic parallel lines was derived,by which the obtained result conformed to that standard value calculated from geodetic latitude,and it is applicable in the range of 400 km from north to south.Therefore,it lays the foundation for establishing the differential equation and differential relationship based on this type of coordinate parameters;and consequently,it is convenient and accurate enough to operate on the ellipsoidal surface in this new form of geodetic coordinate system.
