scholarly journals Analysis of projectile motion with quadratic air resistance from a nonzero height using the Lambert W function

2017 ◽  
Vol 11 (2) ◽  
pp. 328-331 ◽  
Author(s):  
Chokri Hadj Belgacem
Keyword(s):  
Lambert W Function ◽  
Projectile Motion ◽  
Air Resistance

Projectile Motion with Resistance and the Lambert W Function

2004 ◽  
Vol 35 (5) ◽  
pp. 337-350 ◽  
Author(s):  
Edward W. Packel ◽  
David S. Yuen
Keyword(s):  
Lambert W Function ◽  
Projectile Motion

scholarly journals Parabolic Sandwiches for Functions on a Compact Interval and an Application to Projectile Motion

2019 ◽  
Vol 2019 ◽  
pp. 1-7 ◽  
Author(s):  
Robert Kantrowitz ◽  
Michael M. Neumann
Keyword(s):  
Present Article ◽  
Decisive Role ◽  
Valid Argument ◽  
Quadratic Polynomials ◽  
New Approach ◽  
Projectile Motion ◽  
Full Result ◽  
Air Resistance ◽  
Special Case ◽  
Natural Way

About a century ago, the French artillery commandant Charbonnier envisioned an intriguing result on the trajectory of a projectile that is moving under the forces of gravity and air resistance. In 2000, Groetsch discovered a significant gap in Charbonnier’s work and provided a valid argument for a certain special case. The goal of the present article is to establish a rigorous new approach to the full result. For this, we develop a theory of those functions which can be sandwiched, in a natural way, by a pair of quadratic polynomials. It turns out that the convexity or concavity of the derivative plays a decisive role in this context.

Approximate trajectories for projectile motion with air resistance

1998 ◽  
Vol 66 (1) ◽  
pp. 34-37 ◽  
Author(s):  
Michael A. B. Deakin ◽  
G. J. Troup
Keyword(s):  
Projectile Motion ◽  
Air Resistance

Analysis of linear resisted projectile motion using the Lambert W function

2011 ◽  
Vol 223 (2) ◽  
pp. 441-447 ◽  
Author(s):  
H. Hu ◽  
Y. P. Zhao ◽  
Y. J. Guo ◽  
M. Y. Zheng
Keyword(s):  
Lambert W Function ◽  
Projectile Motion

Optimization of projectile motion under linear air resistance

2015 ◽  
Vol 64 (3) ◽  
pp. 365-382 ◽  
Author(s):  
Robert Kantrowitz ◽  
Michael M. Neumann
Keyword(s):  
Projectile Motion ◽  
Air Resistance

scholarly journals The English Galileo and His Vision of Projectile Motion under Air Resistance

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Robert Kantrowitz ◽  
Michael M. Neumann
Keyword(s):  
Classical Mechanics ◽  
Concave Function ◽  
Flight Path ◽  
Projectile Motion ◽  
Air Resistance

This article presents a detailed discussion of the shape of the trajectory traced by a projectile under the forces of gravity and air resistance. In particular, our results confirm the insight of the English scientist Thomas Harriot into the motion of a projectile before the development of Newtonian classical mechanics. Our approach is based on the fact that the flight path of a resisted projectile is implemented by a strictly concave function for which the derivative is also strictly concave.

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