Some purely radial motions with drag

Summary

Some academic results in the field of nonlinear mechanics are here presented. Specifically, exact solutions of the equations of motion for a body moving purely radially in nonlinear central fields of force are given, when the drag of the (homogeneous) medium is taken into account. The drag is assumed to be proportional to the velocity, and several types of forces, including gravitation, are considered. Next, for a nonhomogeneous atmosphere, we assume a density function that may represent the earth's atmosphere and a drag law consisting of two terms (linear and cubic in the velocity), and obtain the solution for a particular case.