Singularities of non-holonomic constraints degeneration and controllability

Mathematics. Physics. Mechanics


Zakalyukin I. V.

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia


We consider the asymptotic behavior of controllable mechanical generic system with linear non-holonomic constraints in a vicinity of the submanifold where the rank of of the system of the constraint equation falls down by one.
We show that if the control parameters are the generalized forces bounded by some constant, then the attainability domain for arbitrary initial point does not contain the neighbourhood of this submanifold. On the other hand, the control kinematic system determined by the same constraint equations is completely controllable.
An example of a system with degeneration of linear constraints is considered. The system consists of a heavy beam with two attached sleighs.


control mechanical system; degeneration of non-holonomic constraints; slow fast variables

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