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Archive of Applied Mechanics

, Volume 89, Issue 4, pp 639–647 | Cite as

Is Newton’s law of motion really of integer differential form?

  • John T. KatsikadelisEmail author
Original
  • 87 Downloads

Abstract

In this investigation, an answer is given to the question of whether Newton’s law of motion is of integer or non-integer, i.e., fractional, order differential form. The answer is given by seeking Newton’s law of motion in the form of a fractional differential operator. Then, applying an identification procedure using separately virtual Galileo’s experimental data on the inclined plane and Kepler’s laws of planetary motion, the fractional differential operator is established yielding the equation of motion. Both identifications yield the law of motion in the form of a fractional differential equation, which is converted into a second-order differential equation, verifying thus that for a body with constant mass Newton’s law of motion is indeed of integer differential form.

Keywords

Newton’s law of motion Integer form Galileo’s experimental data Kepler’s laws of motion System identification Fractional differential form 

Notes

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Structural Analysis, School of Civil EngineeringNational Technical University of AthensAthensGreece

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