Generalized Orbitals under the Influence of 2D Central and Noncentral Forces
Author(s)
Haiduke Sarafian*
ABSTRACT
In polar coordinate system, we consider fifteen classes of forces resulting in unlimited undiscovered orbitals. The classic conic orbits are one of the special subclasses of the fifteen classes. Among the rest of the forces, we show a few instances displaying typical fresh orbitals. Aside from the common theoretical foundation, the specifics of the orbitals are given by the solution of corresponding equations of motion. These are coupled nonlinear differential equations. Solving these equations numerically, utilizing a Computer Algebra System such as Mathematica is conducive to the orbits. Simulation of the orbitals provides a visual understanding about the motion under the influence of the generalized noncentral forces.
In polar coordinate system, we consider fifteen classes of forces resulting in unlimited undiscovered orbitals. The classic conic orbits are one of the special subclasses of the fifteen classes. Among the rest of the forces, we show a few instances displaying typical fresh orbitals. Aside from the common theoretical foundation, the specifics of the orbitals are given by the solution of corresponding equations of motion. These are coupled nonlinear differential equations. Solving these equations numerically, utilizing a Computer Algebra System such as Mathematica is conducive to the orbits. Simulation of the orbitals provides a visual understanding about the motion under the influence of the generalized noncentral forces.
Cite this paper
Sarafian, H. (2014) Generalized Orbitals under the Influence of 2D Central and Noncentral Forces. World Journal of Mechanics, 4, 303-308. doi: 10.4236/wjm.2014.410030.
Sarafian, H. (2014) Generalized Orbitals under the Influence of 2D Central and Noncentral Forces. World Journal of Mechanics, 4, 303-308. doi: 10.4236/wjm.2014.410030.
References
[1] Sarafian, H. (2014) Central Conservative Forces and Orbits beyond Conic Sections, Progress on Difference Equations. Abstract Book, 58, Izmir University of Economics, Turkey. [2] Sarafian, H., Takato, S., and Kaneko, M. (2014) Central Conservative Forces and Orbits beyond Conic Sections. The Journal of Mathematics and System Sciences, 4, 579-585.
www.davidpublishing.org/journals_info.asp?jId=2039 [3] Thronton, S. and Marion, J. (2003) Classical Dynamics of Particles and Systems. 5th Edition, Cengage Learning, Boston. [4] Symon, K.R. (1965) Mechanics. 2nd Edition, Addison-Wesley, New York. [5] Wolfram, S., (2012) Mathematica: A Computational Software Program Based on Symbolic Mathematics, V9.0. [6] Goldstein, H., Safko, J. and Poole, C. (2001) Classical Mechanics. 3rd Edition, Addison-Wesley, New York. [7] Arya, A.P. (1990) Introduction to Classical Mechanics. Allyn and Bacon, London.
[1] Sarafian, H. (2014) Central Conservative Forces and Orbits beyond Conic Sections, Progress on Difference Equations. Abstract Book, 58, Izmir University of Economics, Turkey. [2] Sarafian, H., Takato, S., and Kaneko, M. (2014) Central Conservative Forces and Orbits beyond Conic Sections. The Journal of Mathematics and System Sciences, 4, 579-585.
www.davidpublishing.org/journals_info.asp?jId=2039 [3] Thronton, S. and Marion, J. (2003) Classical Dynamics of Particles and Systems. 5th Edition, Cengage Learning, Boston. [4] Symon, K.R. (1965) Mechanics. 2nd Edition, Addison-Wesley, New York. [5] Wolfram, S., (2012) Mathematica: A Computational Software Program Based on Symbolic Mathematics, V9.0. [6] Goldstein, H., Safko, J. and Poole, C. (2001) Classical Mechanics. 3rd Edition, Addison-Wesley, New York. [7] Arya, A.P. (1990) Introduction to Classical Mechanics. Allyn and Bacon, London.