Hamilton's equations are the equations defined by
where 
and 
is fluxion notation and 
is the so-called Hamiltonian,. These equations frequently
arise in problems of celestial mechanics.
The vector form of these equations is
(Zwillinger 1997, p. 136; Iyanaga and Kawada 1980, p. 1005).
Another formulation related to Hamilton's equation is
 |
(5)
|
where 
is the so-called Lagrangian.
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References
Iyanaga, S. and Kawada, Y. (Eds.). Encyclopedic Dictionary of Mathematics. Cambridge, MA: MIT Press, p. 1005, 1980.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.Zwillinger, D. Handbook
of Differential Equations, 3rd ed. Boston, MA: Academic Press, 1997.Referenced
on Wolfram|Alpha
Hamilton's Equations
Cite this as:
Weisstein, Eric W. "Hamilton's Equations."
From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/HamiltonsEquations.html
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