Integral of Motion
A constant of motion may be defined in a given force field as any function of phase-space coordinates (position and velocity, or position and momentum) and time that is constant throughout a trajectory. A subset of the constants of motion are the integrals of motion, defined as any functions of only the phase-space coordinates that are constant along an orbit. Every integral of motion is a constant of motion, but the converse is not true because a constant of motion may depend on time. Examples of integrals of motion are the angular momentum vector, or a Hamiltonian without time dependence, such as . An example of a function that is a constant of motion but not an integral of motion would be the function for an object moving at a constant speed in one dimension.
Read more about this topic: Constant Of Motion
Famous quotes containing the words integral and/or motion:
“An island always pleases my imagination, even the smallest, as a small continent and integral portion of the globe. I have a fancy for building my hut on one. Even a bare, grassy isle, which I can see entirely over at a glance, has some undefined and mysterious charm for me.”
—Henry David Thoreau (1817–1862)
“subways, rivered under streets
and rivers . . . in the car
the overtone of motion
underground, the monotone
of motion is the sound
of other faces, also underground—”
—Hart Crane (1899–1932)