Showing papers on "Elliptic coordinate system published in 1991"

Axisymmetric difference operators in an orthogonal coordinate system

Abstract: A differential-difference scheme approximating the non-steady axisymmetric equations of gas-dynamics in an arbitrary coordinate system is constructed The scheme is completely conservative

Elliptic orbit coordinate calculator

Abstract: PURPOSE:To calculate the coordinates of an elliptic orbit whose areal velocity is fixed at high-speed with simple configuration and high accuracy by defining coordinates whose cumulative area exceeds a divided area, as the elliptic orbit coordinates with the fixed areal velocity. CONSTITUTION:A divided area calculating means 2 calculates the inputted areal velocity as the divided area of an ellipse equipped with long and short axes A and B, and a cumulative area calculating means 4 cumulatively calculates partial areas to be formed between adjacent lattice points and a center (Xc, Yc) for each elliptic coordinate to be shown by an expression I to be outputted by an elliptic coordinate calculating means 3 which decides elliptic coordinates on the lattice points by successive calculation in respect to the inputted center (Xc, Yc) and the long and short axes A and B. A divided area An calculated by the divided area calculating means 2 is compared with a cumulative area Aacj-1 successively calculated by the cumulative area calculating means 4, and coordinates (Xj+1, Yj+1), which cumulative area A2cj-1 exceeds the divided area An, are defined as the elliptic orbit coordinates with the fixed areal velocity. Thus, the elliptic orbit coordinates with the fixed areal velocity can be calculated at high speed with the simple configuration and high accuracy.

The potential for a homogeneous cylinder in a cylindrical coordinate system

Abstract: Some special cases of the potential for a homogeneous cylinder in a cylindrical coordinate system may be treated by virtue of simple integrals, for example, the potential for a straight rod or wire segment and that for a homogeneous cylinder at the point on its axis. However, because of the involved mathematical operations, the analytical formula of the potential for a homogeneous cylinder at an arbitrary point has not been seen from others. In order to solve the problem, the author has taken the following steps: (1) expanding Green's function elk],x -r'/|r'-r| in the cylindrical coordinate system; (2) transforming Green's function elk'r _r|/|r' r| into Green's function l/|r' r| by setting the wave number k to be zero and integrating the separated azimuthal function cos\"('-); (3) using the integral recursion relation for the function r'2m+1/[(z' z)2 + r'2 + r2](4m+I)/2 with respect to r and those for the functions l/[(z'-z)2 + r2](2m_1)/2 and l/[(z/-z)2-i-r2-(-a2](4m_2/_1)/'2 with respect to z , then we can complete the integrals for the function 1 /1 r' — r| and obtain the analytical expression of the potential for the cylinder in the cylindrical coordinate system. For numerical comparison, we have calculated the potentials for the cylinder and the prolate or oblate spheroid with equivalent volume and same high aspect ratio at far field point. The results are satisfactory.