Nonlinear mathematical models for paths maintaining constant normal accelerations

Pakdemirli M., Ylldlz V.

11th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences, ICNPAA 2016, La Rochelle, France, 4 - 08 July 2016, vol.1798, (Full Text) identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 1798
  • Doi Number: 10.1063/1.4972713
  • City: La Rochelle
  • Country: France
  • Manisa Celal Bayar University Affiliated: Yes

Abstract

New path equations maintaining constant normal accelerations with arbitrary tangential decelerations for a moving object is derived. The case of tangential deceleration proportional to the square of velocity is treated in detail. It is assumed that in this special case, the vehicle is under the influence of drag force only. The equation is cast into a dimensionless form first. Numerical solution of the resulting nonlinear third order differential equation is contrasted with the perturbation solution. When the perturbation parameter is small, the match is excellent. The derived paths may found applications in the motion of land, marine and aerial vehicles.