Hamilton's Equations

The equations defined by

			(1)
			(2)

where  and  is fluxion notation and  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

			(3)
			(4)

(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.

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.