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The dynamics of systems with servoconstraints. II. (English) Zbl 1353.70012
Regul. Chaotic Dyn. 20, No. 4, 401-427 (2015); translation in Nelineĭn. Din. 11, No. 3, 579-611 (2015).
Summary: This paper addresses the dynamics of systems with servoconstraints where the constraints are realized by controlling the inertial properties of the system. Vakonomic systems are a particular case. Special attention is given to the motion on Lie groups with left-invariant kinetic energy and a left-invariant constraint. The presence of symmetries allows the dynamical equations to be reduced to a closed system of differential equations with quadratic right-hand sides. As the main example, we consider the rotation of a rigid body with a left-invariant servo-constraint, which implies that the projection of the body’s angular velocity on some body-fixed direction is zero.
For Part I see [Regul. Chaotic Dyn. 20, No. 3, 205–224 (2015); translation in Nelineĭn. Din. 11, No. 2, 353–376 (2015; Zbl 1353.70036)].

MSC:
70E18 Motion of a rigid body in contact with a solid surface
34C40 Ordinary differential equations and systems on manifolds
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