Restricted Three-Body Problem in Cylindrical Coordinates System

Affiliation(s)

Department of Astronomy, Faculty of Science, King Abdul Aziz University, Jeddah, Saudi Arabia.

Department of Mathematics, Faculty of Science, King Abdul Aziz University, Jeddah, Saudi Arabia.

Department of Astronomy, Faculty of Science, King Abdul Aziz University, Jeddah, Saudi Arabia.

Department of Mathematics, Faculty of Science, King Abdul Aziz University, Jeddah, Saudi Arabia.

ABSTRACT

In this paper, the equations of motion for spatial restricted circular three body problem will be established using the cylindrical coordinates. Initial value procedure that can be used to compute both the cylindrical and Cartesian coordinates and velocities is also developed.

In this paper, the equations of motion for spatial restricted circular three body problem will be established using the cylindrical coordinates. Initial value procedure that can be used to compute both the cylindrical and Cartesian coordinates and velocities is also developed.

Cite this paper

M. Sharaf and A. Alshaery, "Restricted Three-Body Problem in Cylindrical Coordinates System,"*Applied Mathematics*, Vol. 3 No. 8, 2012, pp. 907-909. doi: 10.4236/am.2012.38134.

M. Sharaf and A. Alshaery, "Restricted Three-Body Problem in Cylindrical Coordinates System,"

References

[1] J. Binney and S. Tremaine, “Galactic Dynamics,” Princeton University Press, Princeton, 1987.

[2] C. D. Murray and S. F. Dermott, “Solar System Dynamics,” Cambridge University Press, Cambridge, 1999.

[3] M. A. Sharaf, M. R. Arafah and M. E. Awad, “Prediction of Satellites in Earth’s Gravitational Field with Axial Symmetry Using Burdet’s Regularized Theory,” Earth, Moon and Planets, Vol. 38, No. 1, 1987, pp. 21-36. doi:10.1007/BF00115934

[4] M. A. Sharaf, M. E. Awad and S. A. Najmuldeen, “Motion of Artificial Satellites in the Set of Eulerian Redundant ParametersIII,” Earth, Moon and Planets, Vol. 56, 1992, pp. 141-164.

[5] M. A. Sharaf and A. A. Sharaf, “Motion of Artificial Earth Satellites in the General Gravity Field Using KS Regularized Theory,” Bulletin of the Faculty of Science, Vol. 63, 1995, pp. 157-181.

[6] M. A. Sharaf and A. A. Sharaf, “Closest Approach in Universal Variables,” Celestial Mechanics and Dynamical Astronomy, Vol. 69, No. 4, 1998, pp. 331-346. doi:10.1023/A:1008223105130

[7] E. L. Stiefel and G. Scheifele, “Linear and Regular Celestial Mechanics,” Springer-Verlag, Berlin, 1971.

[8] V. Szebehely, “Theory of Orbits,” Academic Press, New York, 1967.

[1] J. Binney and S. Tremaine, “Galactic Dynamics,” Princeton University Press, Princeton, 1987.

[2] C. D. Murray and S. F. Dermott, “Solar System Dynamics,” Cambridge University Press, Cambridge, 1999.

[3] M. A. Sharaf, M. R. Arafah and M. E. Awad, “Prediction of Satellites in Earth’s Gravitational Field with Axial Symmetry Using Burdet’s Regularized Theory,” Earth, Moon and Planets, Vol. 38, No. 1, 1987, pp. 21-36. doi:10.1007/BF00115934

[4] M. A. Sharaf, M. E. Awad and S. A. Najmuldeen, “Motion of Artificial Satellites in the Set of Eulerian Redundant ParametersIII,” Earth, Moon and Planets, Vol. 56, 1992, pp. 141-164.

[5] M. A. Sharaf and A. A. Sharaf, “Motion of Artificial Earth Satellites in the General Gravity Field Using KS Regularized Theory,” Bulletin of the Faculty of Science, Vol. 63, 1995, pp. 157-181.

[6] M. A. Sharaf and A. A. Sharaf, “Closest Approach in Universal Variables,” Celestial Mechanics and Dynamical Astronomy, Vol. 69, No. 4, 1998, pp. 331-346. doi:10.1023/A:1008223105130

[7] E. L. Stiefel and G. Scheifele, “Linear and Regular Celestial Mechanics,” Springer-Verlag, Berlin, 1971.

[8] V. Szebehely, “Theory of Orbits,” Academic Press, New York, 1967.