Approximate Solution of Sensitivity Matrix with Final Velocity Constraint Using Linear Time-Varying Gravity Assumption

Jalali Naini, S. H.

Approximate Solution of Sensitivity Matrix with Final Velocity Constraint Using Linear Time-Varying Gravity Assumption

Author

S. H. Jalali Naini

Abstract

In this research, an approximate solution of the required velocity with final velocity constraint is derived using linear gravity assumption along the path of current position to the final position vectors. Moreover, an approximate solution for sensitivity matrix of the required velocity with respect to the position vector is obtained. The presented solutions are given for a predetermined final time. In this case, for the free final position, the analytical solution is rather more difficult than its fixed final position counterpart. Therefore, three approaches are utilized for approximation of the final position vector. Finally, the obtained solutions are compared to exact numerical one for the spherical-Earth model.

Keywords

requrired velocity

sensitivity matrix

implicit guidance

Article Title Persian

حل تقریبی ماتریس حساسیت با قید بردار سرعت برای شتاب جاذبة خطی با زمان

Author Persian

سید حمید جلالی نائینی

Abstract Persian

در این تحقیق، حل تقریبی بردار سرعت لازم با قید بردار سرعت با فرض شتاب جاذبة خطی بین موقعیت فعلی و موقعیت نهایی ارائه شده‌است. در ادامه، حل تحلیلی ماتریس حساسیت بردار سرعت لازم نسبت به بردار موقعیت به‌دست می‌آید. حل‌های مذکور به ازای زمان نهایی از پیش‌تعیین حاصل شده‌است. آزاد بودن موقعیت نهایی در این مسئله، حل تحلیلی را نسبت به مسائل با قید بردار موقعیت نهایی، دشوارتر می‌کند. بنابراین، برای محاسبة بردار موقعیت نهایی از سه تقریب استفاده شده‌است. در نهایت، حل‌های به‌دست آمده با حل دقیق برای مدل زمین کروی مقایسه شده‌ است.

Keywords Persian

سرعت لازم

ماتریس حساسیت

هدایت ضمنی

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