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Application of the Frobenius theorem to determination of potentials with their gradients orthogonal to vector fields

Kaczorek T.

Poznan University of Technology Academic Journals. Electrical Engineering

2007

No 56

7-12

The problem of finding potentials of the vector field those gradients are orthogonal to the given vector fields is formulated and solved. The solution to the problem is based on the Frobenius theorem. It is shown that the problem has a solution if and only if the distribution spanned on the vector fields is involutive. A procedure for finding of the desired potentials is proposed and demonstrated on an example of finding one potential for two given vector fields.