with domains 0 [less than or equal to] r < [infinity], 0 [less than or equal to] 0 < [pi], 0 [less than or equal to] [phi] < 2 [pi], so that axis z in cartesian coordinates
becomes the polar axis in spherical polar coordinates.
In order to further improve the computing accuracy of the elements GQ12 and GQ12M, a new method for establishing the local Cartesian coordinate
system and calculating the derivatives of the shape function with respect to the local coordinates is presented in this paper.
29) and (30), we use the following relations for unit vector transformations between the polar and Cartesian coordinates
The machining program was generated using Cartesian coordinates
in the base coordinate system and by the employing linear interpolation between each point on the trajectory.
6]-equivariance of system (1) allows us to study the flow in only one sextant of the phase space in cartesian coordinates
, the behaviour in the rest of the phase space being identical.
Other important features of this unit include the measurement of the distance between an obstacle and an unmanned air object, the computation of the obstacle's position within Cartesian coordinates
and the estimation of the relative velocity of the obstacle.
The normal coordinates are obtained by diagonalization of the matrix of second derivatives of the potential with respect to the mass-weighted Cartesian coordinates
and evaluation at the minimum of the potential .
Log-Polar transform is to transform an image from Cartesian Coordinates
(x, y) to Polar coordinates (y, [theta]) first, then to Log coordinates ([rho], [theta]).
One is defined in Cartesian coordinates
with a linear unidirectional modulation in space, while the other is defined in polar coordinates according to the Bessel cylindrical function (1,2), forming a concentric pattern with the maximum luminance in the center, and gradually decreasing toward the periphery.
Laffoley writes about Utopic Space, which "has no natural directions such as those associated with Cartesian coordinates
To reveal this relation we replace the cartesian coordinates
(x, y) with the polar coordinates (r.
The integral area can be transformed from Cartesian coordinates
to polar coordinates as show in Fig.
When the correction is not taken into account, then the calculated Cartesian coordinates
of point C trajectory would not match with the recorded measurement data
The center of a spheroid is located at origin O and has the Cartesian coordinates
(xo, y0, zo) in O'x'y'z', and the major axis is along the z axis of Oxyz.
projection of the Cartesian coordinates
onto the surface of the new reference ellipsoid.