# Conservative force

conservativenon-conservativenon-conservative forceconservative force fieldconservative forcesconservative systemconservative'' forcenon-conservative forcesnonconservative force
A conservative force is a force with the property that the total work done in moving a particle between two points is independent of the taken path.wikipedia
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### Mechanical energy

mechanicalconservation of mechanical energyenergy
If a force is conservative, it is possible to assign a numerical value for the potential at any point and conversely, when an object moves from one location to another, the force changes the potential energy of the object by an amount that does not depend on the path taken, contributing to the mechanical energy and the overall conservation of energy.
The principle of conservation of mechanical energy states that in an isolated system that is only subject to conservative forces, the mechanical energy is constant.

### Potential energy

potentialpotential energiesgravitational potential
If a force is conservative, it is possible to assign a numerical value for the potential at any point and conversely, when an object moves from one location to another, the force changes the potential energy of the object by an amount that does not depend on the path taken, contributing to the mechanical energy and the overall conservation of energy.
Forces derivable from a potential are also called conservative forces.

### Work (physics)

workmechanical workwork-energy theorem
A conservative force is a force with the property that the total work done in moving a particle between two points is independent of the taken path.
:The work of forces generated by a potential function is known as potential energy and the forces are said to be conservative.

### Scalar potential

potentialpotential functionpotential field
If a force is conservative, it is possible to assign a numerical value for the potential at any point and conversely, when an object moves from one location to another, the force changes the potential energy of the object by an amount that does not depend on the path taken, contributing to the mechanical energy and the overall conservation of energy.
Those that do are called conservative, corresponding to the notion of conservative force in physics.

### Friction

coefficient of frictionstatic frictionfriction coefficient
Gravitational force is an example of a conservative force, while frictional force is an example of a non-conservative force. The gravitational force, spring force, magnetic force (according to some definitions, see below) and electric force (at least in a time-independent magnetic field, see Faraday's law of induction for details) are examples of conservative forces, while friction and air drag are classical examples of non-conservative forces. Examples of nonconservative forces are friction and non-elastic material stress.
Friction is a non-conservative force - work done against friction is path dependent.

### Force field (physics)

force fieldforce fieldsfield of force
A force field F, defined everywhere in space (or within a simply-connected volume of space), is called a conservative force or conservative vector field if it meets any of these three equivalent conditions:
For a conservative force field, it is also independent of the path itself, depending only on the starting and ending points.

### Conservative vector field

irrotationalconservativeconservative field
A force field F, defined everywhere in space (or within a simply-connected volume of space), is called a conservative force or conservative vector field if it meets any of these three equivalent conditions:
If the vector field associated to a force \mathbf{F} is conservative, then the force is said to be a conservative force.

### Conservation of energy

law of conservation of energyenergyenergy conservation law
If a force is conservative, it is possible to assign a numerical value for the potential at any point and conversely, when an object moves from one location to another, the force changes the potential energy of the object by an amount that does not depend on the path taken, contributing to the mechanical energy and the overall conservation of energy.

### Hooke's law

spring constantforce constantelasticity tensor
The gravitational force, spring force, magnetic force (according to some definitions, see below) and electric force (at least in a time-independent magnetic field, see Faraday's law of induction for details) are examples of conservative forces, while friction and air drag are classical examples of non-conservative forces.

### Lorentz force

magnetic forceLorentz force lawLorentz
The gravitational force, spring force, magnetic force (according to some definitions, see below) and electric force (at least in a time-independent magnetic field, see Faraday's law of induction for details) are examples of conservative forces, while friction and air drag are classical examples of non-conservative forces.

### Coulomb's law

Coulomb forceelectrostatic forceCoulomb interaction
The gravitational force, spring force, magnetic force (according to some definitions, see below) and electric force (at least in a time-independent magnetic field, see Faraday's law of induction for details) are examples of conservative forces, while friction and air drag are classical examples of non-conservative forces.

The gravitational force, spring force, magnetic force (according to some definitions, see below) and electric force (at least in a time-independent magnetic field, see Faraday's law of induction for details) are examples of conservative forces, while friction and air drag are classical examples of non-conservative forces.

### Drag (physics)

dragaerodynamic dragair resistance
The gravitational force, spring force, magnetic force (according to some definitions, see below) and electric force (at least in a time-independent magnetic field, see Faraday's law of induction for details) are examples of conservative forces, while friction and air drag are classical examples of non-conservative forces.

### Heat

heat energythermalhot
Usually the energy is turned into heat, for example the heat generated by friction.

### Sound

audiosound wavesound waves
In addition to heat, friction also often produces some sound energy.

### Wake

boat wakesKelvin wake patternboat wake
The water drag on a moving boat converts the boat's mechanical energy into not only heat and sound energy, but also wave energy at the edges of its wake.

### Second law of thermodynamics

second lawsecond2nd law of thermodynamics
These and other energy losses are irreversible because of the second law of thermodynamics.

### Simply connected space

simply connectedsimply-connectedmultiply connected
A force field F, defined everywhere in space (or within a simply-connected volume of space), is called a conservative force or conservative vector field if it meets any of these three equivalent conditions:

### Gravity

gravitationgravitationalgravitational force
Gravitational force is an example of a conservative force, while frictional force is an example of a non-conservative force. The gravitational force, spring force, magnetic force (according to some definitions, see below) and electric force (at least in a time-independent magnetic field, see Faraday's law of induction for details) are examples of conservative forces, while friction and air drag are classical examples of non-conservative forces.

### Stress (mechanics)

stressstressestensile stress
Examples of nonconservative forces are friction and non-elastic material stress.

### Degrees of freedom (physics and chemistry)

degrees of freedomdegree of freedomdegrees of freedom (
Despite conservation of total energy, non-conservative forces can arise in classical physics due to neglected degrees of freedom or from time-dependent potentials.

### General relativity

general theory of relativitygeneral relativity theoryrelativity
General relativity is non-conservative, as seen in the anomalous precession of Mercury's orbit.

### Tests of general relativity

confirmedanomalous precessionclassical tests of general relativity
General relativity is non-conservative, as seen in the anomalous precession of Mercury's orbit.

### Stress–energy–momentum pseudotensor

Landau–Lifshitz pseudotensorEinstein pseudotensorenergy-momentum complex
However, general relativity does conserve a stress–energy–momentum pseudotensor.

### Van der Pol oscillator

Van der Pol equationVan der Polcertain differential equations
In dynamics, the Van der Pol oscillator is a non-conservative oscillator with non-linear damping.