Liouville,s Phase Space Theorem
المؤلف:
Chavel, I
المصدر:
Riemannian Geometry: A Modern Introduction. New York: Cambridge University Press, 1994.
الجزء والصفحة:
...
11-10-2021
1497
Liouville's Phase Space Theorem
States that for a nondissipative Hamiltonian system, phase space density (the area between phase space contours) is constant. This requires that, given a small time increment 
,
the Jacobian be equal to one:
Expressed in another form, the integral of the Liouville measure,
 |
(9)
|
is a constant of motion. Symplectic maps of Hamiltonian systems must therefore be area preserving (and have determinants equal to 1).
REFERENCES:
Chavel, I. Riemannian Geometry: A Modern Introduction. New York: Cambridge University Press, 1994.
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