Regiões de segurança em lançamento de projéteis

Abstract

Nosso principal objetivo neste trabalho é a determinação de regiões de segurança em balística. Por região de segurança entendemos a região do espaço tridimensional que fica livre da ação de projéteis. A determinação da região de segurança será reduzida ao cálculo da envoltória de uma família de trajetórias, indexada segundo o ângulo de tiro.

On the trajectories of projectiles depicted in early ballistic woodcuts

“…The angle α max which maximizes the range of a projectile is found from the angle for which dR/dα = 0. Finding the angle that leads to an explicit expression for α max is however not a simple case of differentiating (20) and setting the result equal to zero before solving for α. Instead, it requires a few subtle algebraic manoeuvres and we follow a procedure first advanced by Groetsch and Cipra in [2].…”

“…The horizontal distance travelled by the projectile on ascent to its peak therefore approaches the upper bound for its range. That this must be the case can be seen by approximating (20) directly. As γ v 0 /g sin α 1, we have ζ 1.…”

“…Thus, e −ζ and hence −ζ e −ζ rapidly tend to zero for increasing ζ . In this limit, the Lambert W function terms appearing in (20) can be approximated by the first term in its series expansion (A.3). Here…”

Some remarks on projectile motion with a linear resistance force

“…In [6][7][8][9][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34] it is obtained, by means of approximate procedures or through computational tools, the trajectory of the particle, the time of flight, the maximum height, the range, the curve of safety or the path length. On the other hand, in the last two decades, the interest in the projectile motion with a retarding force proportional to the velocity has increased because it is a good scenario to apply the Lambert W function since it is necessary to solve transcendental equations in this problem.…”