Notes_Iex%20BP - Iex 1 Examples 3D Representations Example...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
Only variable Examples – 3D Representations Example 1: Given : 1 1 ˆˆ ˆ 1.6772 1.6772 2.3719 ˆ 3.1574 2.4987 0.4658 km/s rR x R y R z vx y z ⊕⊕ =−+ =++ Find : ,,, , , aei ωθ Ω Analysis : Shape Æ 11 1 1 rr vv == 2 1 1 22 3 v ar aR μμ =− = = E hrv Æ ( ) 2 1 hh p a e = Æ e = 0.2 From conic equation Æ Iex 1 Could we check to see if elliptical? 2 c < 1 1 1 1 cos 1 p er θ ∗− ⎧⎫ ⎛⎞ ⎪⎪ ⎨⎬ ⎜⎟ ⎝⎠ ⎩⎭
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Numerical values orbit orientations Æ ˆ ˆˆ ˆ .5 .5 .7071 rv hx y z × == + + × 11 1 ˆ ˆ ˆ ˆ ............. ............. ˆ ............. ............. ˆ IR i i iii Cr h x ss yc s zs s s c c θθ θ Ω Ω .7071 45 i ci =⇒ = ± D .5 i Ω =− .5 i cs Ω −= + quadrant check! Note that we can also obtain the remaining elements of the direction cosine matrix 1 1 1 ˆ .5 .5 .7071ˆ ˆ ˆ ˆ .7071 .7071 r rx y z r hr x y + = + Iex 2 Careful! Generally , are not perpendicular Check unit magnitude
Background image of page 2
1 r ± 1 1 .7071 0 i i ss sc θ = = 1 90 θ= D Back to 1 Recall () 11 1 1 1 ˆˆ vv r r v θθ =+ ii ˆ vr i Æ if 1 0 r > ± ascending if 1 0 r < ± descending in this case 1 .659 0 r → > ± 1 135 ⇒= + D Iex 3
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
UNITS!!
Background image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 12/22/2010 for the course A&AE 532 taught by Professor Kathleenhowell during the Spring '10 term at Purdue University-West Lafayette.

Page1 / 7

Notes_Iex%20BP - Iex 1 Examples 3D Representations Example...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online