# Hamiltonian function

## Hamiltonian function

[‚ham·əl′tō·nē·ən ¦fəŋk·shən]
(mechanics)
A function of the generalized coordinates and momenta of a system, equal in value to the sum over the coordinates of the product of the generalized momentum corresponding to the coordinate, and the coordinate's time derivative, minus the Lagrangian of the system; it is numerically equal to the total energy if the Lagrangian does not depend on time explicitly; the equations of motion of the system are determined by the functional dependence of the Hamiltonian on the generalized coordinates and momenta.
References in periodicals archive ?
1) is said to be Hamiltonian if the right-hand side can be written as v (x) = [omega] (x) (dH (x)) where H (x) is the Hamiltonian function and [omega] (x) is the Poisson bi-vector (i.
4) is the expression for the conservation of the Hamiltonian function.
The periodic behaviour depends on the properties of the Hamiltonian function that are assigned using free parameters.
We design a control law such that the strict feedback control system is forced to behave like a Hamiltonian system with Hamiltonian function (or Hamiltonian) H(x).
is a classical generic Hamiltonian function, expressed in the canonical phase-space variables {p, q}, the total variation (in a vector space [E.
We define the conjugate function of L, named the Hamiltonian function, such H(t,k,p) = [sup.
The parameters A and B are defined as in equation (12), while J, recall, is the Hamiltonian function from the representative firm's dynamic optimization problem.
By introducing a Lagrange multiplier, [lambda](t), the constraint is adjoined to the performance index to define the Hamiltonian function or Pontryagin H function
Using PMP, the problem of optimizing the cost functional [PHI] in (1) can be reformulated into optimizing the Hamiltonian function H(t) as follows (Bryson and Ho, 1975):
defining, respectively, the Hamiltonian function and the conjugate momenta.
A non-autonomous SHS is given by time-dependent Hamiltonian functions [H.
Rozmus, A symplectic integration algorithm for separable Hamiltonian functions, J.

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