The long jump record revisited

1986 ◽  
Vol 28 (2) ◽  
pp. 246-259 ◽  
Author(s):  
Neville de mestre
Keyword(s):  
Mathematical Model ◽  
Analytical Solutions ◽  
Perturbation Analysis ◽  
Computer Time ◽  
Centre Of Mass ◽  
Numerical Schemes ◽  
Modified Model ◽  
Athletic Coaches ◽  
Approximate Analytical Solutions ◽  
Long Jump

AbstractA mathematical model is presented in which the long Jump is treated as the motion of a projectile under gravity with slight drag. The first two terms of a perturbation solution are obtained and are shown to be more accurate than earlier approximate analytical solutions. Results from the perturbation analysis are just as accurate as results from various numerical schemes, and require far less computer time.The model is modified to include the observation that a long-jumper's centre of mass is forward of his feet at take-off and behind his feet on landing.The modified model is used to determine the take-off angle for the current world long jump record, resulting in several interesting observations for athletic coaches.

Approximate analytical solutions of stability problems for skew plates under combined loading

2011 ◽  
Vol 54 (2) ◽  
pp. 115-124 ◽  
Author(s):  
N. I. Akishev ◽  
I. I. Zakirov ◽  
V. A. Ivanov ◽  
V. N. Paimushin ◽  
M. A. Shishov
Keyword(s):  
Analytical Solutions ◽  
Combined Loading ◽  
Stability Problems ◽  
Approximate Analytical Solutions

Approximate analytical solution for the propagation of shock wave in a mixture of small solid particles and non-ideal gas: isothermal flow

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Gorakh Nath
Keyword(s):  
Shock Wave ◽  
Analytical Solutions ◽  
Order Approximation ◽  
Fluid Pressure ◽  
Strong Shock ◽  
Cylindrical Symmetry ◽  
Solid Particles ◽  
Approximate Analytical Solutions ◽  
Axis Of Symmetry ◽  
Physical Variables

Abstract This paper presents the development of mathematical model to obtain the approximate analytical solutions for isothermal flows behind the strong shock (blast) wave in a van der Waals gas and small solid particles mixture. The small solid particles are continuously distributed in the mixture and the equilibrium conditions for flow are maintained. To derive the analytical solutions, the physical variables such as density, pressure, and velocity are expanded using perturbation method in power series. The solutions are derived in analytical form for first approximation, and for second order approximation the set of differential equations are also obtained. The effects of an increase in the problem parameters value on the physical variables are investigated for first order approximation. A comparison is also, made between the solution of cylindrical shock and spherical shock. It is found that the fluid density and fluid pressure become zero near the point or axis of symmetry in spherical or cylindrical symmetry, respectively, and therefore a vacuum is created near the point or axis of symmetry which is in tremendous conformity with the physical condition in laboratory to generate the shock wave.

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