An analytic solution of projectile motion with the quadratic resistance law using the homotopy analysis method

@article{Yabushita2007AnAS,
  title={An analytic solution of projectile motion with the quadratic resistance law using the homotopy analysis method},
  author={Kazuki Yabushita and Mariko Yamashita and Kazuhiro Tsuboi},
  journal={Journal of Physics A: Mathematical and Theoretical},
  year={2007},
  volume={40},
  pages={8403 - 8416}
}
We consider the problem of two-dimensional projectile motion in which the resistance acting on an object moving in air is proportional to the square of the velocity of the object (quadratic resistance law). It is well known that the quadratic resistance law is valid in the range of the Reynolds number: 1 × 103 ∼ 2 × 105 (for instance, a sphere) for practical situations, such as throwing a ball. It has been considered that the equations of motion of this case are unsolvable for a general… 

Figures and Tables from this paper

An Application of Homotopy Analysis to the Viscous Flow Past a Circular Cylinder

The calculated drag coefficients at 6th-order approximation are found to agree reasonably well with experimental measurements and buttresses the usefulness of the homotopy analysis method (HAM) as an important tool in solving highly nonlinear problems.

An analytic solution to the equations of the motion of a point mass with quadratic resistance and generalizations

The paper is devoted to the motion of a body in a fluid under the influence of gravity and drag. Depending on the regime considered, the drag force can exhibit a linear, quadratic or even more

An analytic solution to the equations of the motion of a point mass with quadratic resistance and generalizations

The paper is devoted to the motion of a body in a fluid under the influence of gravity and drag. Depending on the regime considered, the drag force can exhibit a linear, quadratic or even more

Approximate Analytical Description of the Projectile Motion with a Quadratic Drag Force

In this paper, the problem of the motion of a projectile thrown at an angle to the horizon is studied. With zero air drag force, the analytic solution is well known. The trajectory of the projectile

Optimal q-homotopy analysis method for time-space fractional gas dynamics equation

Abstract.It is well known that the homotopy analysis method is one of the most efficient methods for obtaining analytical or approximate semi-analytical solutions of both linear and non-linear

Trajectory of a body in a resistant medium: an elementary derivation

A didactical exposition of the classical problem of the trajectory determination of a body, subject to the gravity in a resistant medium, is proposed. Our revisitation aims to show a derivation of

Modified Homotopy Analysis Method for Nonlinear Aeroelastic Behavior of Two Degree-of-Freedom Airfoils

In this paper, the homotopy analysis method (HAM) is extended to deal with the nonlinear aeroelastic problem of a two degree-of-freedom (DOF) airfoil. To avoid determination of the parameter for the

Newton’s equation of motion with quadratic drag force and Toda’s potential as a solvable one

The family of exactly solvable potentials for Newton’s equation of motion in the one-dimensional system with quadratic drag force has been determined completely. The determination is based on the

Highly accurate analytic formulae for projectile motion subjected to quadratic drag

The classical phenomenon of motion of a projectile fired (thrown) into the horizon through resistive air charging a quadratic drag onto the object is revisited in this paper. No exact solution is

Approximate Analytical Investigation of Projectile Motion in a Medium with Quadratic Drag Force

The classic problem of the motion of a point mass (projectile) thrown at an angle to the horizon is reviewed. The air drag force is taken into account in the form of a quadratic function of velocity
...

References

SHOWING 1-10 OF 17 REFERENCES

Projectile motion with air resistance quadratic in the speed

We consider two‐dimensional motion of a projectile experiencing a constant gravitational force and a fluid drag force which is quadratic in the projectile’s speed. The equations of motions are

Comparison between the HAM and HPM solutions of thin film flows of non-Newtonian fluids on a moving belt

In this paper, we prove in general that the homotopy perturbation method (HPM) proposed in 1998 is only a special case of the homotopy analysis method (HAM) profound in 1992 when ħ = −1. Besides, by

Derivation of the Adomian decomposition method using the homotopy analysis method

  • F. Allan
  • Mathematics
    Appl. Math. Comput.
  • 2007

Series Solutions of Unsteady Boundary‐Layer Flows over a Stretching Flat Plate

  • S. Liao
  • Mathematics, Engineering
  • 2006
An analytic technique, namely, the homotopy analysis method, is applied to give series solution of the unsteady boundary‐layer flows over an impermeable stretching plate. Different from all previous

Hodograph: A useful geometrical tool for solving some difficult problems in dynamics

The hodograph is very useful for solving complicated problems in dynamics. By simple geometrical arguments students can directly obtain the answer to problems that would otherwise be complicated

A Second-Order Approximate Analytical Solution of a Simple Pendulum by the Process Analysis Method

A new king of analytical method of non linear problem called the process analysis method (PAM) is described. The PAM does not depend on the small parameter supposition and therefore can overcome the