Properties
A central force is a conservative field, that is, it can always be expressed as the negative gradient of a potential:
(the upper bound of integration is arbitrary, as the potential is defined up to an additive constant).
In a conservative field, the total mechanical energy (kinetic and potential) is conserved:
(where ṙ denotes the derivative of r with respect to time, that is the velocity), and in a central force field, so is the angular momentum:
because the torque exerted by the force is zero. As a consequence, the body moves on the plane perpendicular to the angular momentum vector and containing the origin, and obeys Kepler's second law. (If the angular momentum is zero, the body moves along the line joining it with the origin.)
As a consequence of being conservative, a central force field is irrotational, that is, its curl is zero, except at the origin:
Read more about this topic: Central Force
Famous quotes containing the word properties:
“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)
“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)