spherical coordinate system and its transformation to cartesian or rectangular and cylindrical coordinate system

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.

Unit Vectors:

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”

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