We present a geometric characterization of the nonlinear smooth functions V:ℝ→ℝ for which the origin is a global isochronous center for the scalar equation x¨=−V′(x) . We revisit Stillinger and Dorignac isochronous potentials V and show a new simple explicit family. Implicit examples are easily produced.
Global isochronous potentials
GORNI, Gianluca;
2013-01-01
Abstract
We present a geometric characterization of the nonlinear smooth functions V:ℝ→ℝ for which the origin is a global isochronous center for the scalar equation x¨=−V′(x) . We revisit Stillinger and Dorignac isochronous potentials V and show a new simple explicit family. Implicit examples are easily produced.File in questo prodotto:
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