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

• Autorzy: Kaczorek T.
• Konferencja: Computer Applications in Electrical Engineering 2007 / sympozjum [12th; April 16-18, 2007; Poznan]
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Frobenius theorem; determination of potentials; potential with gradient orthogonal to vector fields

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Poznan University of Technology Academic Journals. Electrical Engineering
• Rocznik: 2007
• Tom: No 56
• Strony: 7--12
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Kaczorek T.

• Bialystok Technical University

Bibliografia

• [1]Isidori A.: Nonlinear Control Systems, Springer Verlag, Berlin, 1989.
• [2]Marino R., Tomei P.: Nonlinear Control Design - geometric, adaptive, robust, Prentice Hall, London, 1995.
• [3]Jakubczyk B., Respondek W.: On linearization of central systems, Bull. Acad. Polon. Sci. Ser. Sci. Math, 1980, vol. 28, pp. 517-522.
• [4]Kaczorek T., Dzieliński A., Dąbrowski W. i Łopatka R.: The basis of control theory, WNT Warszawa 2006 (in polish).
• [5]Jordan A., Nowacki P.: Global linearization of non linear state equations, Inform. J. Appl. Electromagnetics and Mechanics, vol. 19, 2004, pp. 637-642.
• [6]Kaczorek T., Jordan A.: Global linearization of a class of non linear systems, Comp. Appl. in Electrical Engineering, 2006, pp. 1-8.