Explicitly computing geodetic coordinates from Cartesian coordinates
نویسندگان
چکیده
منابع مشابه
Explicitly computing geodetic coordinates from Cartesian coordinates
This paper presents a new form of quartic equation based on Lagrange’s extremum law and a Groebner basis under the constraint that the geodetic height is the shortest distance between a given point and the reference ellipsoid. A very explicit and concise formulae of the quartic equation by Ferrari’s line is found, which avoids the need of a good starting guess for iterative methods. A new expli...
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Transforming geocentric Cartesian coordinates (X, Y, Z) to geodetic curvilinear coordinates (φ, λ, h) on a biaxial ellipsoid is one of the problems used in satellite positioning, coordinates conversion between reference systems, astronomy and geodetic calculations. For this purpose, various methods including Closed-form, Vector method and Fixed-point method have been developed. In this paper, a...
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The inverse transformation of coordinates, from Cartesian to curvilinear geodetic, or symbolically (x,y,z)-(l,j,h) has been extensively researched in the geodetic literature. However, published formulations require that the application must be deterministically implemented point-by-point individually. Recently, and thanks to GPS technology, scientists have made available thousands of determinat...
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How neurons in the primary motor cortex control arm movements is not yet understood. Here we show that the equations of motion governing reaching simplify when expressed in spatial coordinates. In this fixed reference frame, joint torques are the sums of vector cross products between the spatial positions of limb segments and their spatial accelerations and velocities. The consequences that fol...
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The explicit multi-instanton solutions by ’tHooft and Jackiw, Nohl & Rebbi are generalized to curvilinear coordinates. The idea is that a gauge transformation can notably simplify the expressions obtained after the change of variables. The gauge transform generates a compensating addition to the gauge potential of pseudoparticles. Singularities of the compensating field are irrelevant for physi...
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ژورنال
عنوان ژورنال: Earth, Planets and Space
سال: 2013
ISSN: 1343-8832,1880-5981
DOI: 10.5047/eps.2012.09.009