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:
“An ... important antidote to American democracy is American gerontocracy. The positions of eminence and authority in Congress are allotted in accordance with length of service, regardless of quality. Superficial observers have long criticized the United States for making a fetish of youth. This is unfair. Uniquely among modern organs of public and private administration, its national legislature rewards senility.”
—John Kenneth Galbraith (b. 1908)
“The reason why men enter into society, is the preservation of their property; and the end why they choose and authorize a legislative, is, that there may be laws made, and rules set, as guards and fences to the properties of all the members of the society: to limit the power, and moderate the dominion, of every part and member of the society.”
—John Locke (1632–1704)