نوع مقاله : مقالة‌ تحقیقی‌ (پژوهشی‌)

نویسندگان

دانشکدۀ مهندسی مکانیک، دانشگاه تربیت مدرس، تهران، ایران

چکیده

در این مقاله، حل تقریبی سرعت لازم با قید بردار موقعیت نهایی در مدل زمین بیض یگون با استفاده از فرض شتاب گرانش تک های خطی ارائه شد ه است. در این روش، زمان پرواز به چند بازة زمانی تقسیم و شتاب گرانش در هر بازه به صورت خطی تقریب زده م یشود. این روش حل به یک رابطة صریح سهبعدی برحسب بردار موقعیت کنونی، بردار موقعیت نهایی مطلوب و زمان پرواز منجر خواهد شد. دقت و بار محاسباتی روش یادشده به ازای تعداد باز ههای مختلف با استفاده از حل عددی مسئله به دست آمده و با دو روش تکرارپذیر زارچان و خط یسازی مقایسه شده است. این روش در مقایسه با دو روش یادشده، به ازای بار محاسباتی نسبتاً یکسان، در مدل زمین بیض یگون و مدار حداقل انرژی تا زاویة برد 18 درجه دقت بیشتری دارد. به علاوه، روش ارائه شده برای مسئلة دو یا چند جسم و محاسبة ماتریس حساسیت سرعت لازم قابل استفاده است.

کلیدواژه‌ها

عنوان مقاله [English]

Approximate Solution of Required Velocity in Elliptical Earth Model Using Piecewise Linear

نویسندگان [English]

  • Mohsen Dehghani Mohammad-Abadi
  • Seyed Hamid Jalali Naini

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

چکیده [English]

In this paper, an approximate solution of required velocity with final position constraint is derived using a piecewise linear gravity assumption for elliptical earth model. In this approach, the total flight time is divided into several time intervals and the gravitational acceleration is assumed to be linear at each interval. The solution gives an explicit relation in terms of the current position vector, desired final position and flight time in three dimensions. The accuracy and computational burden of the method are obtained numerically in terms of the number of time intervals, and compared with linearized solution and Zarchan's iterative algorithm. Numerical solution shows that the present method has better accuracy than the two mentioned approaches with the same computational burden up to a range angle of 18 deg for minimum energy trajectory in an elliptical earth model. The presented method can be extended for two or multi-body problem and also for the computation of sensitivity matrix of required velocity.

کلیدواژه‌ها [English]

  • Required velocity
  • Elliptical earth
  • Piecewise linear gravity
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