Analytical and Numerical Solutions of Normal Force Curves with Constant Magnitudes - Pakdemirli, Mehmet (Journal of Applied Nonlinear Dynamics, 2026)
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.