Circular motion of a particle under friction and hydraulic dissipation


  • Giovanni Mingari Scarpello
  • Daniele Ritelli



A heavy particle travels along a rough circular path on a horizontal plane. Launched with a non-zero initial speed, due to the absence of other acting forces, but in presence of friction, it will slow down and eventually stop. The relevant transient is then solved in terms of the Jacobian elliptic functions of the time. Hydraulic air drag is the considered and the new resulting motion is ruled by the first order nonlinear ODE

$$ \dot{w}=-r\,w^{2}-C\,\sqrt{1+w^{4}}, $$

$ (r,C)>0 $, which is solved by means of the first kind Appell-Picard hypergeometric function of two variables $ F_{1}(a,b,b^{\prime };c;x,y)$.

Author Biographies

Giovanni Mingari Scarpello

Libero Universit`a di Bolzano, Facolt`a di Economia, via Sernesi 1, 39100 Bolzano, Italy.

Daniele Ritelli

Dipartimento di matematica per le scienze economiche e sociali, viale Filopanti, 5 40126 Bologna Italy.




How to Cite

Scarpello, G. M., & Ritelli, D. (2005). Circular motion of a particle under friction and hydraulic dissipation. Tamkang Journal of Mathematics, 36(1), 1–16.




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