{{Short description, none
List of things named after
William Rowan Hamilton
Sir William Rowan Hamilton LL.D, DCL, MRIA, FRAS (3/4 August 1805 – 2 September 1865) was an Irish mathematician, astronomer, and physicist. He was the Andrews Professor of Astronomy at Trinity College Dublin, and Royal Astronomer of Irela ...
:
*
Cayley–Hamilton theorem
In linear algebra, the Cayley–Hamilton theorem (named after the mathematicians Arthur Cayley and William Rowan Hamilton) states that every square matrix over a commutative ring (such as the real or complex numbers or the integers) satisfies ...
*
Hamilton's equations
Hamiltonian mechanics emerged in 1833 as a reformulation of Lagrangian mechanics. Introduced by Sir William Rowan Hamilton, Hamiltonian mechanics replaces (generalized) velocities \dot q^i used in Lagrangian mechanics with (generalized) ''momenta ...
*
Hamilton's principle
In physics, Hamilton's principle is William Rowan Hamilton's formulation of the principle of stationary action. It states that the dynamics of a physical system are determined by a variational problem for a functional based on a single function, ...
*
Hamilton–Jacobi equation
In physics, the Hamilton–Jacobi equation, named after William Rowan Hamilton and Carl Gustav Jacob Jacobi, is an alternative formulation of classical mechanics, equivalent to other formulations such as Newton's laws of motion, Lagrangian mecha ...
**
Hamilton–Jacobi–Bellman equation In optimal control theory, the Hamilton-Jacobi-Bellman (HJB) equation gives a necessary and sufficient condition for optimality of a control with respect to a loss function. It is, in general, a nonlinear partial differential equation in the value ...
, related equation in control theory
**
Hamilton–Jacobi–Einstein equation
In general relativity, the Hamilton–Jacobi–Einstein equation (HJEE) or Einstein–Hamilton–Jacobi equation (EHJE) is an equation in the Hamiltonian formulation of geometrodynamics in superspace, cast in the "geometrodynamics era" around t ...
Hamiltonian
In both ''mathematics'' and ''physics'' (specifically ''
mathematical physics
Mathematical physics refers to the development of mathematical methods for application to problems in physics. The '' Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and the developme ...
''):
the term Hamiltonian refers to any energy function defined by a
Hamiltonian vector field In mathematics and physics, a Hamiltonian vector field on a symplectic manifold is a vector field defined for any energy function or Hamiltonian. Named after the physicist and mathematician Sir William Rowan Hamilton, a Hamiltonian vector field is ...
Hamiltonian (control theory) The Hamiltonian is a function used to solve a problem of optimal control for a dynamical system. It can be understood as an instantaneous increment of the Lagrangian expression of the problem that is to be optimized over a certain time period. Ins ...
in
control theory
Control theory is a field of mathematics that deals with the control of dynamical systems in engineered processes and machines. The objective is to develop a model or algorithm governing the application of system inputs to drive the system to a ...
and
Hamiltonian (quantum mechanics)
Hamiltonian may refer to:
* Hamiltonian mechanics, a function that represents the total energy of a system
* Hamiltonian (quantum mechanics), an operator corresponding to the total energy of that system
** Dyall Hamiltonian, a modified Hamiltoni ...
.
In ''physics'' and ''chemistry'':
*
Molecular Hamiltonian
In atomic, molecular, and optical physics and quantum chemistry, the molecular Hamiltonian is the Hamiltonian operator representing the energy of the electrons and nuclei in a molecule. This operator and the associated Schrödinger equation p ...
In ''chemistry'':
*
Dyall Hamiltonian
In quantum chemistry, the Dyall Hamiltonian is a modified Hamiltonian
Hamiltonian may refer to:
* Hamiltonian mechanics, a function that represents the total energy of a system
* Hamiltonian (quantum mechanics), an operator corresponding to the ...
More specifically, as an adjective it is used in the phrases:
In ''mathematical physics'':
*
Hamiltonian flow In mathematics and physics, a Hamiltonian vector field on a symplectic manifold is a vector field defined for any energy function or Hamiltonian. Named after the physicist and mathematician Sir William Rowan Hamilton, a Hamiltonian vector field ...
Hamiltonian mechanics
Hamiltonian mechanics emerged in 1833 as a reformulation of Lagrangian mechanics. Introduced by Sir William Rowan Hamilton, Hamiltonian mechanics replaces (generalized) velocities \dot q^i used in Lagrangian mechanics with (generalized) ''momenta ...
in classical mechanics
*
Hamiltonian optics Hamiltonian opticsH. A. Buchdahl, ''An Introduction to Hamiltonian Optics'', Dover Publications, 1993, . and Lagrangian opticsVasudevan Lakshminarayanan et al., ''Lagrangian Optics'', Springer Netherlands, 2011, . are two formulations of geometrical ...
Hamilton's principle
In physics, Hamilton's principle is William Rowan Hamilton's formulation of the principle of stationary action. It states that the dynamics of a physical system are determined by a variational problem for a functional based on a single function, ...
*
Hamiltonian system
A Hamiltonian system is a dynamical system governed by Hamilton's equations. In physics, this dynamical system describes the evolution of a physical system such as a planetary system or an electron in an electromagnetic field. These systems can ...
*
Hamiltonian vector field In mathematics and physics, a Hamiltonian vector field on a symplectic manifold is a vector field defined for any energy function or Hamiltonian. Named after the physicist and mathematician Sir William Rowan Hamilton, a Hamiltonian vector field is ...
In ''mathematics'':
*
Hamiltonian path
In the mathematical field of graph theory, a Hamiltonian path (or traceable path) is a path in an undirected or directed graph that visits each vertex exactly once. A Hamiltonian cycle (or Hamiltonian circuit) is a cycle that visits each vertex ...
, in graph theory
** Hamiltonian cycle, a special case of a Hamiltonian path
*
Hamiltonian group In group theory, a Dedekind group is a group ''G'' such that every subgroup of ''G'' is normal.
All abelian groups are Dedekind groups.
A non-abelian Dedekind group is called a Hamiltonian group.
The most familiar (and smallest) example of a Hamilt ...
, in group theory
*
Hamiltonian matrix
In mathematics, a Hamiltonian matrix is a -by- matrix such that is symmetric, where is the skew-symmetric matrix
:J =
\begin
0_n & I_n \\
-I_n & 0_n \\
\end
and is the -by- identity matrix. In other words, is Hamiltonian if and only if ...
Hamiltonian constraint
The Hamiltonian constraint arises from any theory that admits a Hamiltonian formulation and is reparametrisation-invariant. The Hamiltonian constraint of general relativity is an important non-trivial example.
In the context of general relativi ...
*
Hamiltonian fluid mechanics Hamiltonian fluid mechanics is the application of Hamiltonian methods to fluid mechanics. Note that this formalism only applies to nondissipative fluids.
Irrotational barotropic flow
Take the simple example of a barotropic, inviscid vorticity-f ...
* Hamiltonian operator, see
Hamiltonian (quantum mechanics)
Hamiltonian may refer to:
* Hamiltonian mechanics, a function that represents the total energy of a system
* Hamiltonian (quantum mechanics), an operator corresponding to the total energy of that system
** Dyall Hamiltonian, a modified Hamiltoni ...
*
Hamiltonian lattice gauge theory
In physics, Hamiltonian lattice gauge theory is a calculational approach to gauge theory and a special case of lattice gauge theory in which the space is discretized but time is not. The Hamiltonian is then re-expressed as a function of degrees ...
By field
In both ''mathematics'' and ''physics'' (specifically ''
mathematical physics
Mathematical physics refers to the development of mathematical methods for application to problems in physics. The '' Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and the developme ...
''):
the term Hamiltonian refers to any energy function defined by a
Hamiltonian vector field In mathematics and physics, a Hamiltonian vector field on a symplectic manifold is a vector field defined for any energy function or Hamiltonian. Named after the physicist and mathematician Sir William Rowan Hamilton, a Hamiltonian vector field is ...
Hamiltonian field theory
In theoretical physics, Hamiltonian field theory is the field-theoretic analogue to classical Hamiltonian mechanics. It is a formalism in classical field theory alongside Lagrangian field theory. It also has applications in quantum field theory ...
*
Hamiltonian flow In mathematics and physics, a Hamiltonian vector field on a symplectic manifold is a vector field defined for any energy function or Hamiltonian. Named after the physicist and mathematician Sir William Rowan Hamilton, a Hamiltonian vector field ...
Hamiltonian system
A Hamiltonian system is a dynamical system governed by Hamilton's equations. In physics, this dynamical system describes the evolution of a physical system such as a planetary system or an electron in an electromagnetic field. These systems can ...
*
Hamiltonian vector field In mathematics and physics, a Hamiltonian vector field on a symplectic manifold is a vector field defined for any energy function or Hamiltonian. Named after the physicist and mathematician Sir William Rowan Hamilton, a Hamiltonian vector field is ...
*
Hamiltonian mechanics
Hamiltonian mechanics emerged in 1833 as a reformulation of Lagrangian mechanics. Introduced by Sir William Rowan Hamilton, Hamiltonian mechanics replaces (generalized) velocities \dot q^i used in Lagrangian mechanics with (generalized) ''momenta ...
in classical mechanics
*
Hamilton's principle
In physics, Hamilton's principle is William Rowan Hamilton's formulation of the principle of stationary action. It states that the dynamics of a physical system are determined by a variational problem for a functional based on a single function, ...
*
Hamilton–Jacobi equation
In physics, the Hamilton–Jacobi equation, named after William Rowan Hamilton and Carl Gustav Jacob Jacobi, is an alternative formulation of classical mechanics, equivalent to other formulations such as Newton's laws of motion, Lagrangian mecha ...
In ''mathematics'' :
*
Hamiltonian path
In the mathematical field of graph theory, a Hamiltonian path (or traceable path) is a path in an undirected or directed graph that visits each vertex exactly once. A Hamiltonian cycle (or Hamiltonian circuit) is a cycle that visits each vertex ...
, in graph theory
** Hamiltonian cycle, a special case of a Hamiltonian path
*
Hamiltonian group In group theory, a Dedekind group is a group ''G'' such that every subgroup of ''G'' is normal.
All abelian groups are Dedekind groups.
A non-abelian Dedekind group is called a Hamiltonian group.
The most familiar (and smallest) example of a Hamilt ...
, in group theory
*
Hamiltonian matrix
In mathematics, a Hamiltonian matrix is a -by- matrix such that is symmetric, where is the skew-symmetric matrix
:J =
\begin
0_n & I_n \\
-I_n & 0_n \\
\end
and is the -by- identity matrix. In other words, is Hamiltonian if and only if ...
* Hamiltonian numbers (or quaternions)
In ''physics'' and ''chemistry'':
* Hamiltonian operator, see
Hamiltonian (quantum mechanics)
Hamiltonian may refer to:
* Hamiltonian mechanics, a function that represents the total energy of a system
* Hamiltonian (quantum mechanics), an operator corresponding to the total energy of that system
** Dyall Hamiltonian, a modified Hamiltoni ...
*
Molecular Hamiltonian
In atomic, molecular, and optical physics and quantum chemistry, the molecular Hamiltonian is the Hamiltonian operator representing the energy of the electrons and nuclei in a molecule. This operator and the associated Schrödinger equation p ...
In ''physics'':
*
Hamiltonian constraint
The Hamiltonian constraint arises from any theory that admits a Hamiltonian formulation and is reparametrisation-invariant. The Hamiltonian constraint of general relativity is an important non-trivial example.
In the context of general relativi ...
*
Hamiltonian fluid mechanics Hamiltonian fluid mechanics is the application of Hamiltonian methods to fluid mechanics. Note that this formalism only applies to nondissipative fluids.
Irrotational barotropic flow
Take the simple example of a barotropic, inviscid vorticity-f ...
*
Hamiltonian lattice gauge theory
In physics, Hamiltonian lattice gauge theory is a calculational approach to gauge theory and a special case of lattice gauge theory in which the space is discretized but time is not. The Hamiltonian is then re-expressed as a function of degrees ...
In ''Chemistry'' :
*
Dyall Hamiltonian
In quantum chemistry, the Dyall Hamiltonian is a modified Hamiltonian
Hamiltonian may refer to:
* Hamiltonian mechanics, a function that represents the total energy of a system
* Hamiltonian (quantum mechanics), an operator corresponding to the ...
In ''control theory'':
*
Hamiltonian (control theory) The Hamiltonian is a function used to solve a problem of optimal control for a dynamical system. It can be understood as an instantaneous increment of the Lagrangian expression of the problem that is to be optimized over a certain time period. Ins ...
*
Hamilton–Jacobi–Bellman equation In optimal control theory, the Hamilton-Jacobi-Bellman (HJB) equation gives a necessary and sufficient condition for optimality of a control with respect to a loss function. It is, in general, a nonlinear partial differential equation in the value ...
Other
* The Hamilton Building at
Trinity College Dublin
, name_Latin = Collegium Sanctae et Individuae Trinitatis Reginae Elizabethae juxta Dublin
, motto = ''Perpetuis futuris temporibus duraturam'' (Latin)
, motto_lang = la
, motto_English = It will last i ...
Hamilton Hamilton may refer to:
People
* Hamilton (name), a common British surname and occasional given name, usually of Scottish origin, including a list of persons with the surname
** The Duke of Hamilton, the premier peer of Scotland
** Lord Hamilt ...