Analytical Investigation of Projectile Motion in Midair

Chudinov, Peter; Eltyshev, Vladimir; Barykin, Yuri

doi:10.24297/jap.v13i6.6167

Cited by 4 publications

(4 citation statements)

References 11 publications

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“…However, those solutions are expressed with quadratures, by meaning that the solutions are expressed with variables that are built from the solution itself. For example, the solution described in [1] is able to give the velocity in function of the slope-angle of the velocity. Because the kernel function can only depend on a given sate and the time-step, implicit solutions cannot be used as kernel function for timeintegration schemes.…”

Section: Previous Workmentioning

confidence: 99%

A robust specialized integration scheme of the projectile motion with quadratic air resistance

Landon¹

2022

Preprint

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A robust and specialized time-integration scheme is proposed for the problem of the motion of a body under a resistive force,acting in the magnitude of the squared velocity of the body. Whereas standard time-integration schemes are well suitable with small time increments, they diverge with large time increments. The specialized time-integration scheme is keeping a good behavior with both small and large time increments.From the analysis of asymptotic behaviors, both near the initial state and far from the initial state, and by reducing the motion of motion into a scalar equation, we proposed an approximation of the solution, that keeps a good behavior both near the initial state and far from the initial state.Finally, we used the obtained approximation to implement a time-integration scheme, that won't diverge on large time increments.We compared the obtained time-integration schemes with other standard time-integration schemes.

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Section: Previous Workmentioning

confidence: 99%

A robust specialized integration scheme of the projectile motion with quadratic air resistance

Landon¹

2022

Preprint

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“…Implicit analytic solutions have already been proposed. The solution described in [1] parameterizes the velocity magnutide with direction angle of the velocity. Even when the proposed solutions can be expressed by elementary functions, they are expressed with parametric variables which are built from trajectory parameters.…”

Section: Previous Workmentioning

confidence: 99%

“…Secondly, we will express the solution in an implicit form, by meaning that the solution is expressed with the solution itself. The equation of motion (1), with the quadratic drag force (3), becomes:…”

Section: Analytic Solution With a Linear Dragmentioning

confidence: 99%

A Convenient Approximation of the Projectile Motion with Quadratic Air Resistance

Landon¹

2021

Preprint

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A convenient approximated analytic solution is proposed for the problem of the motion of a body under a resistive force, acting in the magnitude of the squared velocity of the body. This solution is an explicit function of time, that keeps a good behavior both near the initial state and far from the initial state. To obtain a general analytic solution, we firstly used a reduction principle to be able to manipulate scalar objects, and we analyzed limit behaviors, both near the initial state and far from the initial state. Secondly, we proposed an approximated analytic solution with heuristics based on the built knowledge. Finally, a robust and stable integration scheme is proposed, based on the obtained analytic solution. We compared the scheme with other standard integration schemes.

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“…The force of gravity is always directed vertically downward with mg magnitude, but the force exerted by the air is rather complicated. Because of this, the assumption that this force is simply proportional to the square of the velocity and directed opposite to the direction of motion [1] is an oversimplification of the problem.…”

Section: Introductionmentioning

confidence: 99%

Determination of the drag coefficient by analysing the trajectory of a football

Gábor

2020

MDT

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Two different types of motion were analysed based on video footage using the free software tool named Tracker. One of them involved dropping the football vertically without any spin, the other type was the projectile motion resulted from a goalie punt. The analysis consisted of fitting the time dependence of the coordinates using a sixth order polynomial, then using these functions and other parameters to obtain the drag coefficient as a function of speed and Reynolds number. Similarly to previous works, the drag coefficient showed large differences for the different speeds. The irregularities and asymmetry of the ball also caused the results to be different for the different trials depending on the orientation of the ball, as well as the slight horizontal spin of the ball during its projectile motion. This method can prove to be a useful tool for further studies in a more controlled environment with higher quality new balls.

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Analytical Investigation of Projectile Motion in Midair

Cited by 4 publications

References 11 publications

A robust specialized integration scheme of the projectile motion with quadratic air resistance

A robust specialized integration scheme of the projectile motion with quadratic air resistance

A Convenient Approximation of the Projectile Motion with Quadratic Air Resistance

Determination of the drag coefficient by analysing the trajectory of a football

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