Campus Livre
potential
Potential function of a vector field.
Category: Mathematics > Calculus
Syntax
P = potential(V, X)Finds a scalar function P whose gradient with respect to X is the field V.
Description
A field has a potential only if it is conservative, meaning that the Jacobian of V is symmetric. Then the work along any path depends only on the end points. potential integrates the components one at a time and matches the terms. For [y x] the potential is x*y.
Input arguments
V- Vector of symbolic expressions: the field.
X- Vector of variables with the same length as
V.
Output arguments
P- Symbolic potential, with the constant set to zero.
Example
A conservative field
syms x y
P = potential([y x], [x y])Output
P = x*y