Geodesic
On the dynamics of systems with one-sided non-integrable constraints
Theoretical and applied mechanics, Tome 46 (2019) no. 1.

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In the paper we take the first steps in studying the dynamics of systems with one-sided differential constraints defined by inequalities in the phase space. We give a general definition of motion for systems with such constraints. Within the framework of the classical non-holonomic model, and also for systems with servoconstraints (according to Béghin), we present the conditions under which the system leaves two-sided differential constraints. As an example, we consider the Chaplygin sleigh with a one-sided constraint, which is realized by means of an anisotropic force of viscous friction. Variational principles for the determination of motion of systems with one-sided differential constraints are presented.
Keywords: non-integrable constraints, servoconstraints, non-holonomic mechanics, vakonomic mechanics, one-sided constraint, unilateral constraint 
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Valery V. Kozlov. On the dynamics of systems with one-sided non-integrable constraints. Theoretical and applied mechanics, Tome 46 (2019) no. 1. http://geodesic.mathdoc.fr/item/TAM_2019_46_1_a2/