A Santiago

Modelling the dynamics of bodies self-propelled by exponential mass exhaustion

We present a study of the ascending vertical motion of a self-propelled body under a uniform gravitational field suffering the action of two different types of air friction forces: linear on the velocity, which is valid for slowly moving bodies, and quadratic on the velocity. We study the special case where the thrust force is a decreasing function of mass, which corresponds to the exponential mass exhaustion rate. We present in detail the analytical solutions for the equations of motion for the two types of air friction, and briefly present some techniques for solving the related ordinary differential equations. This paper is intended for undergraduate physics teachers and for graduate students.

Analytical Description of Ascending Motion of Rockets in the Atmosphere.

In continuation of a previous work [1], we present an analytic study of ascending vertical motion of a rocket subjected to a quadratic drag for the case where the mass-variation law is a linear function of time. We discuss the detailed analytical solution of the model differential equations in closed form. Examples of application are presented and discussed. This paper is intended for undergraduate physics teachers and for graduate students.