Hamilton's Equations
The equations defined by
 |  |  | (1) |
 | |  | (2) |
where
and 
is the so-called Hamiltonian, 
are called Hamilton's equations. Theseequations frequently arise in problems of celestial mechanics. Anotherformulation related to Hamilton's equation is | (3) |
is the so-called Lagrangian.
References
Morse, P. M. and Feshbach, H. ``Hamilton's Principle and Classical Dynamics.'' §3.2 in Methods of Theoretical Physics, Part I. New York: McGraw-Hill, pp. 280-301, 1953.
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