scholarly journals On one resolvent method for integrating the low angle trajectories of a heavy point projectile motion under quadratic air resistance

2011 ◽  
Vol 3 (3) ◽  
pp. 265-277 ◽  
Author(s):  
Viktor Vladimirovich Chistyakov
Keyword(s):  
Projectile Motion ◽  
Air Resistance ◽  
Resolvent Method

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

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.

scholarly journals Analytical construction of the projectile motion trajectory in midair

MOMENTO ◽  
2021 ◽  
pp. 79-96
Author(s):  
Peter Chudinov ◽  
Vladimir Eltyshev ◽  
Yuri Barykin
Keyword(s):  
Analytical Solutions ◽  
Initial Conditions ◽  
Resistance Force ◽  
Tennis Ball ◽  
Projectile Motion ◽  
Classic Problem ◽  
Analytical Construction ◽  
Air Resistance ◽  
Wide Range ◽  
Large Period

A classic problem of the motion of a projectile thrown at an angle to the horizon is studied. Air resistance force is taken into account with the use of the quadratic resistance law. An analytic approach is mainly applied for the investigation. Equations of the projectile motion are solved analytically for an arbitrarily large period of time. The constructed analytical solutions are universal, that is, they can be used for any initial conditions of throwing. As a limit case of motion, the vertical asymptote formula is obtained.  The value of the vertical asymptote is calculated directly from the initial conditions of motion. There is no need to study the problem numerically. The found analytical solutions are highly accurate over a wide range of parameters. The motion of a baseball, a tennis ball, and a shuttlecock of badminton are presented as examples.

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