User:Egm6341.s10.team3.sa/Mtg31

Mtg 31: Thu, 18 Mar 10

 Typeset of transparencies, not lecture transcript. Subramanian Annamalai 14:06, 12 August 2010 (UTC)

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HW:
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Derive the following formula for arc length of ellipse using triangle OAB and cosine raw.


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\overset{\frown}{PQ} = \int_{\theta_{P}}^{\theta_{Q}}d\theta\left[r^2+\left(\frac{dr}{d\theta}\right)^{2}\right]^{\frac{1}{2}} $$
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APPLICATION - Engineering: $$\displaystyle \underbrace{Optimal}_{Minimum\,fuel\,-\,Use\,of\,thrusters}\; \underbrace{Trajectory}_{\sum_{i} arc(i)} \; : Earth \rightarrow Mars $$



Trajectory Shaping: Optimal Trajectory as $$\displaystyle \sum_i arc(i) $$ 

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1.SUPERSONIC INTERCEPTOR: Find angle of attack and thrust to reach a given altitude at minimum time. Reference: Bryson and Denham - 1962. 

2.BUNT MANEUVER OF AIRCRAFT: Minimum altitude to reach target with a bunt maneuver.(inverted loop) Reference: Subchan and Zbikowski - 2007 

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