SIAM Review · 2006 · 32 citations · 8 references
Natural SciencesMathematicsPhysicsDifferential EquationsMathematical PhysicsPartial Differential EquationsSchrödinger EquationString TheoryUndergraduate CurriculumWave Equation ModelsWave EquationsWave Propagation In Strings
Following Antman [Amer. Math. Mon., 87 (1980), pp. 359–370], we advocate a more physically realistic and systematic derivation of the wave equation suitable for a typical undergraduate course in partial differential equations. To demonstrate the utility of this derivation, three applications that follow naturally are described: strings, hanging chains, and jump ropes.
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Partial differential equations: analytical solution techniques
Choice Reviews Online · 1990 · 211 citations
The Equations for Large Vibrations of Strings
Stuart S. Antman · American Mathematical Monthly · 1980 · 119 citations
Dynamic Patterns and Self-Knotting of a Driven Hanging Chain
Andrew Belmonte, Michael Shelley, Shaden T. Eldakar et al. · Physical Review Letters · 2001 · 74 citations · Full text
The Equations for Large Vibrations of Strings
Stuart S. Antman · American Mathematical Monthly · 1980 · 71 citations