Nonlinear curve equations maintaining constant normal accelerations with drag induced tangential decelerations

Abstract A nonlinear curve equation is derived for a vehicle exposed to drag force only. At each point on the curve, the vehicle maintains constant normal acceleration component. The resulting curve equation is a highly nonlinear third order ordinary differential equation. By defining dimensionless coordinates, the equation is cast into a non-dimensional form and a special path parameter is defined. Two different perturbation type solutions as well as a series solution are constructed as approximations to the curves. The three approximate solutions are contrasted with the numerical solution of the problem. The validity range of the approximate solutions is discussed. The curves may be used in determining the routes of land, marine and aerial vehicles.