Abstract
The many variants of falling chain problems that have been published in the physics literature over the last two centuries are here analyzed using generalized Euler–Lagrange equations that include momentum flux. Familiar results are recovered, and new ones are presented. We demonstrate and clarify the role played by momentum flux by considering the falling chains as both variable-mass and fixed-mass systems. We calculate the evolution of energy as a useful parameter that provides insight into some of the unexpected behavior of falling chain systems. Our Lagrangian approach incorporates all published falling chain phenomena (including the whiplash effect) within a unifying framework, highlighting connections between the phenomena and providing a valuable pedagogical example of variable mass systems analysis.
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