Geodesic
The dynamics of systems with servoconstraints. II
Russian journal of nonlinear dynamics, Tome 11 (2015) no. 3, pp. 579-611

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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.
Keywords: servoconstraints, symmetries, Lie groups, left-invariant constraints, systems with quadratic right-hand sides, vakonomic systems. 
@article{ND_2015_11_3_a6,
     author = {V. V. Kozlov},
     title = {The dynamics of systems with servoconstraints. {II}},
     journal = {Russian journal of nonlinear dynamics},
     pages = {579--611},
     publisher = {mathdoc},
     volume = {11},
     number = {3},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ND_2015_11_3_a6/}
}
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V. V. Kozlov. The dynamics of systems with servoconstraints. II. Russian journal of nonlinear dynamics, Tome 11 (2015) no. 3, pp. 579-611. http://geodesic.mathdoc.fr/item/ND_2015_11_3_a6/