Further References on Mode Coupling

Recently, a great number of papers were published on the systems exhibiting mode coupling instability due to friction and the complex effect of damping on such systems. See papers by Hoffmann and his coworkers [79-81] and Jezequel and his coworkers [82-89]. Other recent works on this subject include [90-94]. 

In Sect. 3.2, we have seen that a dynamical system with unilateral or bilateral frictional contact can possess a peculiar characteristic, namely the inertia matrix may be asymmetric and nonpositive definite. Painleve was the first to point out the difficulties that may arise in such cases [53, 95]. As we will see in this section through examples, the presence of a kinematic constraint with friction could lead to situations where the equations of motion of the system do not have a bounded solution (inconsistency) or the solution is not unique (indeterminacy). These situations where the existence and uniqueness properties of the solution of the equations of motion are violated are known as the Painleve s paradoxes. There is a vast literature on the general theory of the rigid body dynamics with frictional constraints 

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