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Hamilton's Equations

The equations defined by

$\displaystyle \dot q$ $\textstyle =$ $\displaystyle {\partial H\over\partial p}$ (1)
$\displaystyle \dot p$ $\textstyle =$ $\displaystyle -{\partial H\over\partial q},$ (2)

where $\dot x\equiv dx/dt$ and $H$ 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
p={\partial L\over\partial\dot q},
\end{displaymath} (3)

where $L$ is the so-called Lagrangian.


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.

© 1996-9 Eric W. Weisstein