Paradox of a particle’s trajectory moving on a string
 Bartłomiej Dyniewicz,
 Czesław I. Bajer
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This paper deals with the paradoxical properties of the solution of string vibration under a moving mass. The solutions published to date are not simple enough and cannot be applied to investigations in the entire range of mass speeds, including the overcritical range. We propose a formulation of the problem that allows us to reduce the problem to a secondorder matrix differential equation. Its solution is characteristic of all features of the critical, subcritical, and overcritical motion. Results exhibit discontinuity of the mass trajectory at the end support point, which has not been previously reported in the literature. The closed solution in the case of a massless string is analyzed and the discontinuity is proved. Numerical results obtained for an inertial string demonstrate similar features. Small vibrations are analyzed, which is why the effect discussed in the paper is of purely mathematical interest. However, the phenomenon results in complexity in discrete solutions.
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 Title
 Paradox of a particle’s trajectory moving on a string
 Journal

Archive of Applied Mechanics
Volume 79, Issue 3 , pp 213223
 Cover Date
 20090301
 DOI
 10.1007/s0041900802229
 Print ISSN
 09391533
 Online ISSN
 14320681
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Moving mass
 Vibrations of string
 Inertial load
 Industry Sectors
 Authors

 Bartłomiej Dyniewicz ^{(1)}
 Czesław I. Bajer ^{(1)}
 Author Affiliations

 1. Institute of Fundamental Technological Research, Polish Academy of Sciences, Świętokrzyska 21, 00049, Warsaw, Poland