Motion of a Particle Relative to the Earth

Abstract

Textbooks dealing with this topic are usually content to solve approximately the equations of motion for a particle moving under constant gravity g, using the fact that the angular velocity w of the Earth is small. (See A. S. Ramsey—Dynamics, Part II (§§4.6-4.74) or L. A. Pars—A Treatise on Analytical Dynamics § 10.10.) These equations of motion may be solved exactly, of course, without placing any restriction on w. The modified equations of motion for the particle moving in a medium offering resistance kv per unit mass, v being the velocity of the particle, may also be solved exactly.