The Dynamics of Systems with Servoconstraints. II

    2015, Volume 20, Number 4, pp.  401-427

    Author(s): Kozlov V. V.

    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 servoconstraint, which implies that the projection of the body’s angular velocity on some body-fixed direction is zero.
    Keywords: servoconstraints, symmetries, Lie groups, left-invariant constraints, systems with quadratic right-hand sides, vakonomic systems
    Citation: Kozlov V. V., The Dynamics of Systems with Servoconstraints. II, Regular and Chaotic Dynamics, 2015, Volume 20, Number 4, pp. 401-427

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