Quasi-continuous spatial motion of a mass-spring chain

Philip Rosenau*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The three-dimensional motion of mass-spring chain in close to continuum conditions (a large number of mass-springs per unit length) is shown to be governed by rtt= T(A) Ar5S+ h2 12rsstt, r=(x,y,z), A≡|rS|, where T is the tension function of the continuum (arbitrary but known) and A is the stretch, r is the spatial displacement vector, s is the reference coordinate along the chain and h is equilibrium discreteness length. Some exact solutions for the string (h≡0) and the chain are derived. While the string supports only trivial travelling waves (the stretch must be constant) the chain admits a travelling wave confined to a plane with the stretch propagating as a solitary wave. In general the dispersion born out of the discreteness counteracts the steepening of waves caused by the nonlinearity and leads to the formation of nonlinear structures.

Original languageEnglish
Pages (from-to)224-234
Number of pages11
JournalPhysica D: Nonlinear Phenomena
Issue number1-2
StatePublished - Jul 1987
Externally publishedYes


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