Mechanical oscillators described by a system of differential-algebraic equations

The classical framework for studying the equations governing the motion of lumped parameter systems presumes one can provide
expressions for the forces in terms of kinematical quantities (i.e.
the velocity and the displacement). This is not possible for a very large class of problems where one can only provide implicit relations
between the forces and the kinematical quantitiesIn certain special cases, one can provide non-invertible expressions for a kinematical quantity in terms of the force. Mathematically, this leads to a the
so-called differential algebraic equations; more precisely, a second order ODE coupled with an additional algebraic constraint. We study
several such problems, including the Coulomb friction and some of its generalizations. We prove existence results, and provide both negative and positive results concerning the uniqueness of solutions.

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