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.
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dynamical systems
