@inbook{178f8a086be944648e66fa872ffb36a8,
title = "A closed form solution of the run-time of a sliding bead along a freely hanging slinky",
abstract = "The author has applied Lagrangian formalism to explore the kinematics of a bead sliding along a frictionless, freely hanging vertical Slinky. For instance, we derived a closed analytic equation for the run-time of the bead as a function of the traversed coil number. We have applied Mathematica to animate the 3-dimensional motion of the bead. The derived run-time is incorporated within the animation to clock the bead's actual motion. With the help of Mathematica we have solved the inverse run-time equation and have expressed the traversed coil number as a function of the run-time. The latter is applied to further the analysis of the problem conducive to analytic time-dependent equations for the bead's vertical position, its falling speed and its falling acceleration, and its angular velocity about the symmetry axis of the Slinky. It is also justified that a Slinky is a device capable of converting the gravitational potential energy of a sliding bead into pure rotational energy.",
author = "Haiduke Sarafian",
year = "2004",
doi = "10.1007/978-3-540-25944-2_41",
language = "English (US)",
isbn = "3540221298",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "319--326",
editor = "Marian Bubak and {van Albada}, {Geert Dick} and Sloot, {Peter M. A.} and Dongarra, {Jack J.}",
booktitle = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
address = "Germany",
}