Implicit Guidance Equations in PolarÂ Coordinates

Jalali Naini, Seyed Hamid

Implicit Guidance Equations in PolarÂ Coordinates

Author

Seyed Hamid Jalali Naini

Faculty of Mechanical Engineering, Tarbiat Modares University, Tehran, Iran

Abstract

In this paper, implicit guidance equations are derived in polar coordinates. Depending on applications, implicit guidance equations in polar coordinates may be preferred over cartesian coordinates. Moreover, depending on the type of guidance problem, analytical solutions for sensitivity matrices may be simplified using polar coordinates. Therefore, transformation of implicit guidance equation into polar coordinates can be useful in guidance problems. In addition, the resulting equations are extended to cylindrical coordinates.

Keywords

implicit guidance

Required velocity

sensitivity matrix

Article Title Persian

معادلات هدایت ضمنی در مختصات قطبی

Author Persian

سید حمید جلالی نائینی

دانشکده مهندسی مکانیک، دانشگاه تربیت مدرس، تهران، ایران

Abstract Persian

در این تحقیق، معادلات هدایت ضمنی در مختصات قطبی استخراج شدهاست. بر حسب کاربرد، ممکن است استفاده از هدایت ضمنی در مختصات قطبی بر معادلات هدایت ضمنی در مختصات دکارتی ترجیح دادهشود. همچنین بر حسب نوع مسئله، ممکن است استخراج روابط تحلیلی برای ماتریس حساسیت با استفاده از مختصات قطبی آسا‌‌ن‌تر باشد؛ لذا استخراج این روابط در مختصات قطبی و تبدیل روابط به مختصات دکارتی میتواند مفید باشد. در ادامه نیز نتایج حل به مختصات استوانهای تعمیم داده شدهاست.

Keywords Persian

هدایت ضمنی

سرعت لازم

ماتریس حساسیت

Pitman, G.R., Inertial Guidance, John Wiley & Sons Inc., New York, 1962.
Battin, R.H., “Space Guidance Evolution- A Personal Narrative,” Journal of Guidance, Control, and Dynamics, Vol. 5, No. 2, 1982, pp. 97-110.
Siouris, G.M., Missile Guidance and Control Systems, Springer Verlag, NY, 2004.
Martin, F.H., Closed-Loop Near-Optimum Steering for a Class of Space Missions, (D.Sc. Thesis), Massachusetts Institute of Technology, Cambridge, MA, USA, 1965.
Battin, R.H., An Introduction to the Mathematics and Methods of Astrodynamics, Revised Edition, AIAA Education Series, USA, 1999.
Taylor, A.J. and Wagner, J.T., “On-Board Approach Guidance for a Planet-Orbiter,” Journal of Spacecraft and Rockets, Vol. 3, No. 12, 1966, pp. 1731-1737.
Martin, F.H., “Closed-Loop Near-Optimum Steering for a Class of Space Missions,” AIAA Journal, Vol. 4, No. 11, May 1966, pp. 1920-1927.
Gunckel, T.L., “Explicit Rendezvous Guidance Mechanization,” Journal of Spacecraft and Rockets, Vol. 1, No. 2, 1964, pp. 217-219.
Sokkappa, B.G., “On Optimal Steering to Achieve Required Velocity” Guidance and Control, Proceedings of the 16^th International Astronautical Congress, Edited by M. Lunc, 1966, pp. 105-116.
Culbertson, J.D., “A Steering Law Satisfying the Constant Total Time of Flight Constraint,” Journal of Spacecraft and Rockets, Vol. 4, No. 11, 1967, pp. 1470-1474.
Bhat, M.S. and Shrivastava, S.K., An Optimal Q-Guidance Scheme for Satellite Launch Vehicles, Journal of Guidance, Control, and Dynamics, Vol. 10, No. 1, 1987, pp. 53-60.
Ghahramani, N., Naghash, A. and Towhidkhah, F., “Incremental Predictive Command of Velocity to Be Gained Guidance Method,” Journal of Aerospace Science and Technology, Iranian Aerospace Society, Vol. 5, No. 3, 2008, pp. 99-105.
Kamal, S. A. and Mirza, A, “The Multi-Stage-Q System and the Inverse-Q System for Possible Application in Satellite-Launch Vehicle (SLV), The 4^th International Bhurban Conference on Applied Sciences and Technologies, Bhurban, Pakistan, June 2005.
Jalali-Naini, S.H., “An Implicit Guidance Formulation for Velocity Constraint,” The 9^th Iranian Aerospace Society Conference, Tehran, Feb. 2010.
Battin, R.H., “Lambert’s Problem Revisited,” AIAA Journal, Vol. 15, No. 5, May 1977, pp. 707-713.
Battin, R.H., “An Elegant Lambert Algorithm,” Journal of Guidance, Control, and Dynamics, Vol. 7, No. 6, 1984, pp. 662-670.
Nelson, S.L. and Zarchan, P., “Alternative Approach to the Solution of Lambert’s Problem,” Journal of Guidance, Control, and Dynamics, Vol. 15, No. 4, 1992, 1003-1009.
Izzo, D., “Lambert’s Problem for Exponential Sinusoids,” Journal of Guidance, Control, and Dynamics, Vol. 29, No. 5, 2006, pp. 1242-1245.
Zhang, G., Mortari, D. and Zhou, D., “Constrained Multiple-Revolution Lambert’s Problem,” Journal of Guidance, Control, and Dynamics, Vol. 33, No. 6, 2010, pp. 1779-1786.
Leeghim, H. and Jaroux, B.A., “Energy-Optimal Solution to the Lambert Problem,” Journal of Guidance, Control, and Dynamics, Vol. 33, No. 3, 2010, pp. 1008-1010.
Bando, M. and Yamakawa, H., “New Lambert Algorithm Using the Hamiltonian-Jacobi-Bellman Equation,” Journal of Guidance, Control, and Dynamics, Vol. 33, No. 3, 2010, pp. 1000-1008.