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:
“Somehow we have been taught to believe that the experiences of girls and women are not important in the study and understanding of human behavior. If we know men, then we know all of humankind. These prevalent cultural attitudes totally deny the uniqueness of the female experience, limiting the development of girls and women and depriving a needy world of the gifts, talents, and resources our daughters have to offer.”
—Jeanne Elium (20th century)
“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)