Cases with several and with no solutions of the initial value problem and the corresponding states of systems with friction-affected constraints

Abstract

Owing to the kinetic friction laws, the equations for the computation of the accelerations and reaction forces for given positions and velocities of systems with friction-affected constraints are non-linear. Therefore, cases without, with one or with several sets of solutions can occur. With the help of planar systems with sliding and hinge joints it is shown that several sets of solutions correspond to different modes of contact in the constraints. All sets of solutions can be assigned to physical unequivocal states of the system and can be interpreted as unique solutions of the initial value problem with specified configurations of the system. No solution means that the friction parameters are too large and exceed the values for which friction locking occurs.

Keywords

initial value problem multi-body planar systems sliding and hinge joints with friction

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