In the spherical coordinate system, the three orthogonal surfaces are a sphere, a cone and a plane. P ( d, θ, φ} ) represents a point.
where d represents radius of a sphere or distance from the origin to point P
θ represents the angle of elevation that is angle between z axis at the origin and to point.
φ is the azimuthal angle measured from X- axis.
The unit vectors at a point are di, θj and φ k
where di is perpendicular to spherical surface in increasing d direction.
θj is perpendicular to the surface of cone towards increasing θ.
Φ is perpendicular to the shifted XZ plane in the increasing Φ direction.
The coordinate system is right handed.
Thus cross product of spherical unit vectors is: Continue reading “spherical coordinate system and its transformation to cartesian or rectangular and cylindrical coordinate system”