The energy functional is the total
energy
In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of ...
of a certain system, as a
functional
Functional may refer to:
* Movements in architecture:
** Functionalism (architecture)
** Form follows function
* Functional group, combination of atoms within molecules
* Medical conditions without currently visible organic basis:
** Functional sy ...
of the system's
state
State may refer to:
Arts, entertainment, and media Literature
* ''State Magazine'', a monthly magazine published by the U.S. Department of State
* ''The State'' (newspaper), a daily newspaper in Columbia, South Carolina, United States
* ''Our S ...
.
In the
energy methods of simulating the dynamics of complex structures, a state of the system is often described as an element of an appropriate
function space
In mathematics, a function space is a set of functions between two fixed sets. Often, the domain and/or codomain will have additional structure which is inherited by the function space. For example, the set of functions from any set into a vect ...
. To be in this state, the system pays a certain cost in terms of energy required by the state. This energy is a scalar quantity, a function of the state, hence the term ''functional''. The system tends to develop from the state with higher energy (higher cost) to the state with lower energy, thus local minima of this functional are usually related to the stable stationary states. Studying such states is part of the
optimization problems, where the terms ''energy functional'' or ''cost functional'' are often used to describe the objective function.
Examples
* In
Hamiltonian systems, the energy functional is given by the
Hamiltonian.
See also
*
Action (physics)
In physics, action is a scalar quantity describing how a physical system has changed over time. Action is significant because the equations of motion of the system can be derived through the principle of stationary action.
In the simple case ...
*
Density functional theory
Density-functional theory (DFT) is a computational quantum mechanical modelling method used in physics, chemistry and materials science to investigate the electronic structure (or nuclear structure) (principally the ground state) of many-body ...
*
Hamilton's principle
*
History of variational principles in physics
*
Potential well
A potential well is the region surrounding a local minimum of potential energy. Energy captured in a potential well is unable to convert to another type of energy ( kinetic energy in the case of a gravitational potential well) because it is ca ...
External links
Energy methods in elasticity Wikiversity
Wikiversity is a Wikimedia Foundation project that supports learning communities, their learning materials, and resulting activities. It differs from Wikipedia in that it offers tutorials and other materials for the fostering of learning, rather ...
.
Energy (physics)
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