Andrey I. Rodionov- Candidate of phys. & math. sciences, Associate professor of Novosibirsk State Technical University, Phone: +7(383-2) 46-17-77, e-mail:ajonn.r@mail.ru

Аннотация. Создан формализм, описывающий динамику мехатронных и электромеханических систем с неполными дифференциальными программами движения. Движение таких систем представлено как движение их несвободных Изображающих Точек в пространстве E_3N по многообразию R_S. Получены уравнения движения Изображающей Точки и ковариантные формы уравнений движения. Представлено Расширение теории Максвелла – Лагранжа на электромеханические системы с неполными дифференциальными программами движения. Приведены примеры.

Ключевые слова: Мехатронные и электромеханические системы произвольных порядков; неполные дифференциальные программы движения; произвольные голономные и неголономные связи; разомкнутые модели управления; Изображающая Точка системы; кинэта; обобщённые силовые факторы; уравнения движения Изображающей Точки; аналитические ковариантные формы уравнений движения.

Abstract. Formalism is created to describe the dynamics of mechatronic and electromechanical systems with incomplete differential programs of motion. The motions of such systems are featured as a motion of its constrained Affix in E_3N -space on the diversity of R_S. The Affix motion equations and series of their covariant forms are derived. The Extension of Maxwell – LaGrange theory for electromechanical systems with arbitrary incomplete differential programs of motion is made. Examples are given.

Keywords: Mechatronic and electromechanical systems of arbitrary orders; incomplete differential programs of motion; arbitrary holonomic and nonholonomic constraints; open-looped control systems; Affix; kineta; generalized force factors; the Affix motion equations; analytical covariant forms of motion equations.

References:

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2. Dobronravov V.V. Controllable systems as systems with nonholonomic constraints. "Mechanics", 1961, № 104, p.27-32. (in Russian )

3. Ostromensky P.I., Rodionov A.I. Setting up and investigating the equations of motion of holonomic and nonholonomic systems by method of generalized forces // Scientific bulletin Novosibirsk State Technical University.- 1997- № 3, p.121-140. (in Russian)

4. Rodionov A.I., Kim V.F. Equations, Theorems and Principles of arbitrary order’s nonholonomic dynamics, Proc. of Joint Symp. between Sister Univ. in Mech. Eng. ”Advanced Studies in Mechanical Engineering”, August 22-24, 2002, p. 239-242, Yeungnam, Korea.

5. Rodionov A.I., Kaveshnikov V.M. On dynamics of mechatronic systems with incomplete differential programs of motion, Proc. of the 11^th World Cong. in Mechanism and Machine Science, Vol.3, Mechatronics, April 1-4, 2004, p. 1331-1335, China Machinery Press, Tianjin, China.

6. Rodionov A.I. The equations of analytical dynamics of systems with differential constraints of any orders. Part.1. // Scientific bulletin of the Novosibirsk State Technical University. - 2012. - №4(49). - p.99-106. (in Russian)

7. Rodionov A.I. The equations of analytical dynamics of systems with differential constraints of any orders. Part.2. // Scientific bulletin of the Novosibirsk State Technical University. - 2013. - №3(52). – p.195-202. (in Russian)

8. Rodionov A.I. Covariant forms of the principles and the equations of the motion of systems with differential constraints // Bulletin of the Tomsk Polytechnic University. – 2013. – Vol. 323, № 2. Mathematics and Mechanic. Physics.- p.44-48. (in Russian)

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