Hamilton's Equations
The equations defined by
q^. = (partialH)/(partialp)
(1)
p^. = [画像:-(partialH)/(partialq),]
(2)
where p^.=dp/dt and q^.=dq/dt is fluxion notation and H is the so-called Hamiltonian, are called Hamilton's equations. These equations frequently arise in problems of celestial mechanics.
The vector form of these equations is
q^._i = H_(p_i)(t,q,p)
(3)
p^._i = -H_(q_i)(t,q,p)
(4)
(Zwillinger 1997, p. 136; Iyanaga and Kawada 1980, p. 1005).
Another formulation related to Hamilton's equation is
where L 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 EquationsCite this as:
Weisstein, Eric W. "Hamilton's Equations." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/HamiltonsEquations.html