The Motion of a Heavy Particle in a Medium with Quadratic Drag Force

Abstract

A local analytical solution for the problem of the motion of particle under quadratic drag force was constructed, and analytical formulae for main parameters of particle trajectory were obtained earlier by the present author. In this paper, we consider an application of these formulae. The determination of the motion kinematical parameters and drag coefficient from the measurement results is presented. In contradistinction to those results in open literature, simple analytical formulations for principal functional dependencies of the problem are constructed.

Simple analytical algorithm for constructing the envelope of the projectile trajectories in midair

“…The results of calculations using the formula (11) are presented in table 1. The second column of the table contains range values calculated analytically by the formula (11). The third column of the table contains range values from integration of the equations of motion (1).…”

“…All motion characteristics described by relationships (2) are functions of V 0 , θ 0 , initial conditions of throwing. Relationships (2), in turn, make it possible to obtain simple analytical formulas for six basic functional relationships of the problem which are y(x), y(t), x(t), y(θ), x(θ), t(θ) [11].…”

A Case Study on Projectile Motion

“…Hence, to shape the variables t, x and y we must either complete system(1) numerically or appraise the precise integrals (3). Comparatively single approximate analytical formulas for the principal parameters of tendency of the projectile are deduce in (Chudinov, 2002. The four parameters address to the top of the trajectory, four -to the stage of drip.…”

“…Therefore the converse formulas are competent for the qualitative and quantitative narrative of the motion of the baseball and other resemblant goal. These formulas, in devote, occasion it likely to obtain a uncompounded divisive formula for the principal functional relationship of the proposition y(x) (Chudinov, 2002). In the want of air resistance, the trajectory of a point mass is a parabola.…”

“…This is why the description of the projectile course by means of a single approximate analytical formula under the square mien resistance is of powerful methodological and instructive significance. In (Chudinov, 2002;2013) comparatively harmless approximate analytical formulas have been possess to ponder the motion of the projectile in a medium with a quadratic comfit violence. In this article, these formulas are interest to solve the humanistic problem of maximizing the projectile distance.…”