The classical tautochrone problem involves motion along curves caused by the special potential V(y)=mgy. We use fractional derivatives to find tautochrone curves under arbitrary potentials V(y). We generalize these further to potentials that are functions of two variables V(x,y). An Appendix gives intuitive motivation for the fractional calculus employed.

Topics
Differential geometry, Fractional calculus
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© 1999 American Association of Physics Teachers.
1999
American Association of Physics Teachers
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