Hamilton,s Equations
المؤلف:
Iyanaga, S. and Kawada, Y.
المصدر:
Encyclopedic Dictionary of Mathematics. Cambridge, MA: MIT Press
الجزء والصفحة:
...
12-6-2018
885
Hamilton's Equations
The equations defined by
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
(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.
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