The equations defined by

(1) | |||

(2) |

where and is the so-called Hamiltonian, are called Hamilton's equations. These equations frequently arise in problems of celestial mechanics. Another formulation related to Hamilton's equation is

(3) |

**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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1999-05-25