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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Analytical and Numerical Solutions of Normal Force Curves with Constant Magnitudes

Journal of Applied Nonlinear Dynamics 14(2) (2025) 285--298 | DOI:10.5890/JAND.2025.06.005

Mehmet Pakdemirli

Department of Mechanical Engineering, Manisa Celal Bayar University, Muradiye, Yunusemre, Manisa, Turkey

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Abstract

In a two-dimensional vertical space, the equations determining the paths of a vehicle for which the magnitude of normal reaction force being constant are derived. Two different equations are considered: 1) Constant speed with energy not conserved, 2) Variable speed with energy conserved. The equations are cast in a non-dimensional form for universality of the results. Perturbation solutions, perturbation iteration method solutions (PIM) are derived for each case. In the case of vanishing normal force, instead of the approximate analytical solutions, the exact solutions are given. The approximate analytical solutions are contrasted with the numerical solutions. The critical value of the magnitude of the normal force which transforms the curves from concave-down to concave-up form is derived. It is found that the perturbation iteration solutions conform better to the numerical solutions than the perturbation solutions.

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