Is Newton’s law of motion really of integer differential form?
- 87 Downloads
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.
KeywordsNewton’s law of motion Integer form Galileo’s experimental data Kepler’s laws of motion System identification Fractional differential form
- 2.Newton, I.: The Mathematical Principles of Natural Philosophy; Translated into English by Andrew Motte, published by Daniel Adee, New York (1846)Google Scholar
- 5.Katsikadelis, J.T.: Derivation of Newton’s law of motion from Kepler’s laws of planetary motion. Arch. Appl. Mech. 88(2018), 27–38 (2017). 10.1007/s00419-017-1245-xGoogle Scholar
- 6.Katsikadelis, J.T.: System identification by the analog equation method. In: Brebbia, C.A. (ed.) Boundary Elements XVII, pp. 33–44. Computational Mechanics Publications, Southampton, Boston (1995)Google Scholar
- 7.Katsikadelis, J.T.: Numerical solution of variable order fractional differential equations (2018). arXiv:1802.00519 [math.NA]
- 9.NASA Planetary Comparison Chart, http://solarsystem.nasa.gov/planets/compchart.cfm. (Retrieved 6 June 2015)