Forest UCM Energy CentralForce

A central force is defined as a force depends only on separation distance

[math]\vec{F} = f(\vec r) \hat r[/math]

ie

Coulomb force and gravitation force.

Spherical Coordinates

Forest_UCM_NLM_Ch1_CoordSys#Spherical

The differential change of [math]\vec r[/math] in spherical coordinates occurs in three directions.

In the radial direction

[math]dr \hat r[/math]

In the polar angle direction

[math]r d \theta \hat \theta[/math]

In the aximuthal angle direction

[math]r \sin \phi d \phi \hat \phi[/math]

The differential force of the displacement vector in spherical coordinates is

[math]d \vec r = r dr \hat r + r d \theta \hat \theta + r \sin \phi d \phi \hat \phi[/math]

Gradient in spherical coordinates

Forest_UCM_Energy#Central_Forces