Module 1.6 Relation between Unit Vectors of Various Orthogonal Coordinate Systems

Module 1.6 Relation between Unit Vectors of Various Othogonal Coordinate Systems

(a_x, a_y, a_z) → (a_r, a_φ, a_z)

(a_r, a_φ, a_z) → (a_x, a_y, a_z)

(a_r, a_φ, a_z) → (a_θ, a_φ, a_R)

(a_θ, a_φ, a_R) → (a_r, a_φ, a_z)

a_x a_y a_z

Animation

Cartesian Coordinates: x = (m), y = (m), z = (m).

Cylindrical Coordinates: r = (m), φ = ^o, z = (m).

Spherical Coordinates: R = (m), θ = ^o, φ = ^o.

Introduction:

Axis X：Red arrow
Axis Y：Green arrow
Axis Z：Blue arrow
1. Press the left mouse button and move the mouse cursor to change the viewpoint, or you can click the standard view button in the upper right corner.
2. Press the right mouse button and move the graph with your mouse.

Parameters:

Naming convention I:

Cartesian coordinates Cylindrical coordinates Spherical coordinates
Naming convention II:

Cartesian coordinates Cylindrical coordinates Spherical coordinates