Important Properties
There are many useful features of the effective potential. The condition for a particle of energy E flying by to be `trapped' and go into an orbit:
To find the radius of a circular orbit, we simply minimize the effective potential with respect to, or equivalently set the net force to zero and then solve for :
After solving for, plug this back into to find the maximum value of the effective potential
To find the frequency of small oscillations:
where the double prime indicates the second derivative of the effective potential with respect to .
Read more about this topic: Effective Potential
Famous quotes containing the words important and/or properties:
“... the most important effect of the suffrage is psychological. The permanent consciousness of power for effective action, the knowledge that their own thoughts have an equal chance with those of any other person ... this is what has always rendered the men of a free state so energetic, so acutely intelligent, so powerful.”
—Mary Putnam Jacobi (1842–1906)
“A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.”
—Ralph Waldo Emerson (1803–1882)