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 coordinatesThe 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 [19].

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.