TL;DR
This paper introduces a unified theoretical framework for the dissipative dynamics of one-dimensional continua with singularities, resolving longstanding paradoxes in chain dynamics.
Contribution
It presents a new theory that unifies the treatment of chain problems, successfully resolving paradoxes that have persisted for nearly two centuries.
Findings
Paradoxes in chain dynamics are resolved.
A unified theory for dissipative chain dynamics is developed.
The approach removes previous theoretical inconsistencies.
Abstract
For nearly two centuries the dynamics of chains have offered examples of paradoxical theoretical predictions. Here we propose a theory for the dissipative dynamics of one-dimensional continua with singularities which provides a unified treatment for chain problems that have suffered from paradoxical solutions. These problems are duly solved within the present theory and their paradoxes removed---we hope.
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