The radial, circumferential, and meridional directions must be defined based
on the original coordinates of each node in the node set for which the
transformation is invoked. The global ($X,Y,Z$)
coordinates of the center of the spherical system, a, and
of a point on the polar axis, b, must be given as shown in
Figure 3.

The origin of the local coordinate system is at the node of interest. The
local ${X}^{1}$-axis
is defined by a line through the node and point a. The
local ${Z}^{1}$-axis
lies in a plane containing the polar axis (the line between points
a and b) and is perpendicular to the
local ${X}^{1}$-axis.
The local ${Y}^{1}$-axis
forms a right-handed coordinate system with ${X}^{1}$
and ${Z}^{1}$.

A spherical coordinate system cannot be defined for a node that lies along
the line joining points a and b.

Abaqus/CAE Usage

Any module: : Type: CSYS: select any method, and click OK: Spherical