# Potential Field

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## Potential Field

(also conservative field), a vector field whose circulation around any closed curve is equal to zero. If the potential field is a force field, this implies that the work done by the forces in going around a closed path is equal to zero. For a potential field a(M) there exists a single-valued function u(M), called the potential of the field, such as a = grad u. If the potential field is given in a simply connected region ft, then the potential of this field can be found from the formula

u = ∫AM (a,t) dl

in which AM is any smooth curve connecting the fixed point A of Ω with point M, t is the unit vector tangent to the curve AM, and l is the length of path AM as measured from point A. If a(M) is the potential field, then curl a = 0 (seeCURL). Conversely, if curl a = 0 and the field is given in a simply connected region and is differentiable, then a(M) is a potential field. Examples of potential fields are electrostatic fields, gravitational fields and velocity fields of irrotational flow.

References in periodicals archive ?
Therefore, the resulting potential field consists of the potential fields of obstacles, road lines and road boundaries.
Improved potential field method for unknown obstacle avoidance using UAV in indoor environment.
Caption: Figure 5: Local potential field near the triggering wire in the view of (a) vertical plane and (b) horizontal plane.
Cui, "Dynamic motion planning for mobile robots using potential field method," Autonomous Robots, vol.
No potential field was applied during Experiment A in order to isolate the differences between each control method.
We notice that the variational problem PV is formulated in terms of displacement field, stress field, electrical potential field, electric displacement field and a wear function.
It appears that the effective potential field on the region of interest (between two spheres) resulting from the remote induced charges becomes less effective with each iteration.
2006 Tectonic analysis of northwestern South America from integrated Satellite, airborne and surface potential field anomalies, PhD dissertation, School of Earth Sciences, The Ohio State University, 198p.
The notion an alpha field is associated to any potential field that can be described by two dimensionless field parameters [alpha] and [alpha]'.
An estimated 16-trillion-foot square of natural gas is believed to be present in the potential field.
Prior to the comparatively very expensive exercise of acquisition and analysis of seismic data in the exploration for oil and gas in sedimentary basins it is common practice to conduct preliminary investigations using, for example, potential field (gravity/magnetic) data.

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