Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



On some inverse problems in dynamics

Authors: M. S. Klamkin and D. J. Newman
Journal: Quart. Appl. Math. 26 (1968), 281-283
MSC: Primary 31.11
DOI: https://doi.org/10.1090/qam/234000
MathSciNet review: 234000
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Abstract: It is known that the time of traverse of a freely falling body through a straight tunnel connecting any two points of the surface of a uniform spherical planet is isochronous. We show here that if the isochronous property is to hold for any planet with a spherical symmetric density, then the density must be constant. Also it is shown that if the isochronous property is to hold for any uniform spherical planet subject to a central force law, then the force law must be inverse square. However, the isochronous property can hold for one uniform spherical planet with a different force law of attraction.

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DOI: https://doi.org/10.1090/qam/234000
Article copyright: © Copyright 1968 American Mathematical Society

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