Contour integrals for gravity computation of horizontal 212-D bodies with variable density

Computation of contour integrals

Efficient Gravity Field Computation for Trajectory Propagation near Small Bodies

We present an approximation scheme for gravitational force near arbitrarily shaped small bodies. The approximation uses polynomial interpolation with an adaptive spatial data structure. This data structure allows us to drive errors in the model to within user defined thresholds. The result is a method that is expected to reduce the run time of trajectory integrations around small bodies without...

Performance of SST k-ω Turbulence Model for Computation of Viscous Drag of Axisymmetric Underwater Bodies

This paper presents 2-D finite volume method for computation of viscous drag based on Reynolds-averaged Navier-Stokes (RANS) equations. Computations are performed on bare submarine hull DREA and six axisymmetric bodies of revolution with a number of length-diameter (L/D) ratios ranging from 4 to 10. Both structured and unstructured grids are used to discretize the domain around the bodies. Diff...

3-D Cauchy-type integrals for terrain correction of gravity and gravity gradiometry data

S U M M A R Y Fundamental to complex analysis is the Cauchy integral theorem, and the derivation of Cauchytype integrals. For over 40 yr, Cauchy-type integrals have been used to describe analytical continuation, establish the location of singular points, and study non-single-valued solutions of inverse problems in 2-D potential field theory. In this paper, we revive this interesting and fundame...

The Analysis of Contour Integrals

Recommended by Stephen L. Clark For any n, the contour integral y cosh x ∮ C cosh zs / sinh z − sinhx n 1 dz, s2 −λ, is associated with differential equation d2y x /dx2 λ n n 1 /coshx y x 0. Explicit solutions for n 1 are obtained. For n 1, eigenvalues, eigenfunctions, spectral function, and eigenfunction expansions are explored. This differential equation which does have solution in terms of t...