Journal of Applied Nonlinear Dynamics
A Computational and Theoretical Review on the Motion of a Spinning Spherical Particle in Media with Different Viscosities
Journal of Environmental Accounting and Management 7(4) (2018) 361369  DOI:10.5890/JAND.2018.12.004
F. L. Braga, I. G. Pauli, V. S. Amorim
Coordenadoria de Física, Instituto Federal de Educação, Ciências e Tecnologia do Espírito Santo, Campus Cariacica, Av. José Sette s/n, Espirito Santo, 29150410, Brasil
Download Full Text PDF
Abstract
Ballistic calculations were the first attempt where computers were used for, and the oblique launching of objects when studied at an ideal approach is quite simple with a parabolic trajectory of particles. The same motion could become intrinsically difficult to solve when dissipative forces are considered at the model. The present work shows a brief theoretical review on the motion of a spinning spherical particle under the influence of the gravitational field, the drag force and the Magnus effect. The drag forces can alter the translation speed and the angular velocity. We determined the profiles of the trajectories, velocity field and the modifications of frequency in two scenarios, first when the particle is moving across one medium and second when it pass through one medium to another. The results, trajectories obtained are in agreement the predictions for the cases where non continuous and non uniform forces are acting on a body.
Acknowledgments
We would like to thanks CNPq and CAPES for the financial support and Instituto Federal de Educação, Ciências e Tecnologia do Espírito Santo for the opporunity.
References

[1]  Halliday, D., Resnick, R., and Walker, J. (2010), Fundamentals of Physics, Number v. 1. John Wiley & Sons. 

[2]  Young, H.D., Freedman, R.A., Sandin, T.R., and Ford, A.L. (2000), Sears and Zemansky's University Physics. Number v. 1 in AddisonWesley series in physics. AddisonWesley. 

[3]  Tipler, P.A. and Mosca, G. (2004), Physics for Scientists and Engineers, Number v. 1 in Physics for Scientists and Engineers, W.H. Freeman. 

[4]  Ramalho, F., Ferraro, N.G., and de Toledo Soares, P.A. (2007), Os fundamentos da Física, Number v. 1. Moderna. 

[5]  Yamamoto, K. and Fuke, L.F. (2007), Fisica Para Ensino Medio, Number v. 1. Saraiva  Didáticos. 

[6]  Goldstein, H., Poole, C.P., and Safko, J.L. (2002), Classical Mechanics. Addison Wesley. 

[7]  Thornton, S.T. and Marion, J.B. (2004), Classical Dynamics of Particles and Systems, Brooks/Cole. 

[8]  Fox, R.W., McDonald, A.T., and Pritchard, P.J. (2008), Introduction to Fluid Mechanics, Wiley. 

[9]  Boyce, W.E. and DiPrima, R.C. (2004), Elementary differential equations, Number v. 1. John Wiley. 

[10]  W.H. Press (2007), Numerical Recipes 3rd Edition: The Art of Scientific Computing. Cambridge University Press. 

[11]  Duan, Y., Keefe, M., Bogetti, T.A., Cheeseman, B.A., and Powers, B. (2006), A numerical investigation of the influence of friction on energy absorption by a highstrength fabric subjected to ballistic impact, International Journal of Impact Engineering, 32(8), 12991312. 

[12]  Yigit, K. (2011), Temperature dependent flow softening of titanium alloy Ti6Al4V: An investigation using finite element simulation of machining, Journal of Materials Processing Technology, 211(4), 737749. 

[13]  Soeren, O. and Jakob, M. (2000), An experimental investigation of the relative diffusion of particle pairs in threedimensional turbulent flow, Journal of Fluid Mechanics, 422, 207223. 

[14]  Sandip, P., Johan, P., Niels, D., Alfred, J., Fredrik, I., and Kuipers, J.A.M. (Hans) (2015), Numerical and experimental investigation of induced flow and dropletdroplet interactions in a liquid spray, Chemical Engineering Science, 138, 1730. 

[15]  Barkla, H.M. and Auchterlonie, L.J. (1971), The Magnus or Robins effect on rotating spheres, Journal of Fluid Mechanics, 47, 437447. 

[16]  White, B.R. and Schulz, J.C. (1977), Magnus effect in saltation, Journal of Fluid Mechanics, 81(7), 497512. 

[17]  Seifert, J. (2012), A review of the Magnus effect in aeronautics, Progress in Aerospace Sciences, 55, 1745. 

[18]  Bishop, R.E.D. and Hassan, A.Y. (1964), The lift and drag forces on a circular cylinder in a flowing fluid, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 277(1368), 3250. 

[19]  Pride, S.R., Morgan, F.D., and Gangi, A.F. (1993), Drag forces of porousmedium acoustics, Phys. Rev. B, 47, 49644978. 

[20]  Lei, U., Yang, C.Y., and Wu, K.C. (2006), Viscous torque on a sphere under arbitrary rotation, Applied Physics Letters, 89(18). 