Pick-up, impact and peeling

Abstract eng:
We consider a class of problems involving a one-dimensional, inextensible body with a propagating discontinuity (shock) asso- ciated with partial contact with a rigid obstacle providing steric, frictional, or adhesive forces. This class includes the pick-up and impact of an axially flowing string or cable, and the peeling of an adhesive tape. The dynamics are derived by applying an action principle to a non-material volume. The resulting boundary conditions provide momentum and energy jump conditions at the shock. These are combined with kinematic conditions on velocities and accelerations to obtain families of steady-state solutions parameterized by the shock velocity and momentum and energy sources.

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