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The problems are generally based on the following model: A particular spacecraft can be represented as a single axisymmetric rigid body B. Let n₂ be inertially fixed unit vectors; then, 6, are parallel to central, principal axes. To make the mathematics simpler, introduce a frame C where n₂ = ĉ₁ = b; initially. 6₁ Assume a mass distribution such that J =₁₁• B* •b₁ = 450 kg - m² I = b² •Ï¾˜ • b₂ = b¸ •Ï¾* •b¸ = 200 kg - m² K J-I C³ =r₁₁ = r₁₁ Problem 2: Assume that the body moves in a circular orbit at a constant rate Q. Let â₁ be orbit-fixed unit vectors where a₂ is directed from the orbit center to B*; then â³ is 90° from a₂ in the direction of motion and a₁ is parallel to the orbit normal. a2 The dependent variables in the differential equations that govern motion include the measure numbers @;; the kinematic variables that are the body 1-3-2 angles for orientation of C in A: w₁ = 0 - w₂ = −K@₁w¸ −r@¸ +3KQ² (c₁§¿§¸ − ¤¸§₁ ) ( c₁₂ C₁₂ + § § ₁ ) - ȧ¸ = K@₁₂+r@₂ −3KQ² (c₁₂S₂¤¸ + §3§₁ ) c₁₂ Ó₁ = [(@c₂+w,s¸-rc₁)/c]-Q Ω Ò₂ = − (@₁ − 1 )§³ + @z€3 - 0₁ = {[a,c,-re, +0,5₁] s₂ / c₂} + w₂ (a) Derive the equation for ė₂

The problems are generally based on the following model: A particular spacecraft can be represented as a single axisymmetric rigid body B. Let n₂ be inertially fixed unit vectors; then, 6, are parallel to central, principal axes. To make the mathematics simpler, introduce a frame C where n₂ = ĉ₁ = b; initially. 6₁ Assume a mass distribution such that J =₁₁• B* •b₁ = 450 kg - m² I = b² •Ï¾˜ • b₂ = b¸ •Ï¾* •b¸ = 200 kg - m² K J-I C³ =r₁₁ = r₁₁ Problem 2: Assume that the body moves in a circular orbit at a constant rate Q. Let â₁ be orbit-fixed unit vectors where a₂ is directed from the orbit center to B*; then â³ is 90° from a₂ in the direction of motion and a₁ is parallel to the orbit normal. a2 The dependent variables in the differential equations that govern motion include the measure numbers @;; the kinematic variables that are the body 1-3-2 angles for orientation of C in A: w₁ = 0 - w₂ = −K@₁w¸ −r@¸ +3KQ² (c₁§¿§¸ − ¤¸§₁ ) ( c₁₂ C₁₂ + § § ₁ ) - ȧ¸ = K@₁₂+r@₂ −3KQ² (c₁₂S₂¤¸ + §3§₁ ) c₁₂ Ó₁ = [(@c₂+w,s¸-rc₁)/c]-Q Ω Ò₂ = − (@₁ − 1 )§³ + @z€3 - 0₁ = {[a,c,-re, +0,5₁] s₂ / c₂} + w₂ (a) Derive the equation for ė₂

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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The problems are generally based on the following model: A particular spacecraft can be represented as a single axisymmetric rigid body B. Let n₂ be inertially fixed unit vectors; then, 6, are parallel to central, principal axes. To make the mathematics simpler, introduce a frame C where n₂ = ĉ₁ = b; initially. 6₁ Assume a mass distribution such that J =₁₁• B* •b₁ = 450 kg - m² I = b² •Ï¾˜ • b₂ = b¸ •Ï¾* •b¸ = 200 kg - m² K J-I C³ =r₁₁ = r₁₁
Transcribed Image Text:The problems are generally based on the following model: A particular spacecraft can be represented as a single axisymmetric rigid body B. Let n₂ be inertially fixed unit vectors; then, 6, are parallel to central, principal axes. To make the mathematics simpler, introduce a frame C where n₂ = ĉ₁ = b; initially. 6₁ Assume a mass distribution such that J =₁₁• B* •b₁ = 450 kg - m² I = b² •Ï¾˜ • b₂ = b¸ •Ï¾* •b¸ = 200 kg - m² K J-I C³ =r₁₁ = r₁₁
Problem 2: Assume that the body moves in a circular orbit at a constant rate Q. Let â₁ be orbit-fixed unit vectors where a₂ is directed from the orbit center to B*; then â³ is 90° from a₂ in the direction of motion and a₁ is parallel to the orbit normal. a2 The dependent variables in the differential equations that govern motion include the measure numbers @;; the kinematic variables that are the body 1-3-2 angles for orientation of C in A: w₁ = 0 - w₂ = −K@₁w¸ −r@¸ +3KQ² (c₁§¿§¸ − ¤¸§₁ ) ( c₁₂ C₁₂ + § § ₁ ) - ȧ¸ = K@₁₂+r@₂ −3KQ² (c₁₂S₂¤¸ + §3§₁ ) c₁₂ Ó₁ = [(@c₂+w,s¸-rc₁)/c]-Q Ω Ò₂ = − (@₁ − 1 )§³ + @z€3 - 0₁ = {[a,c,-re, +0,5₁] s₂ / c₂} + w₂ (a) Derive the equation for ė₂
Transcribed Image Text:Problem 2: Assume that the body moves in a circular orbit at a constant rate Q. Let â₁ be orbit-fixed unit vectors where a₂ is directed from the orbit center to B*; then â³ is 90° from a₂ in the direction of motion and a₁ is parallel to the orbit normal. a2 The dependent variables in the differential equations that govern motion include the measure numbers @;; the kinematic variables that are the body 1-3-2 angles for orientation of C in A: w₁ = 0 - w₂ = −K@₁w¸ −r@¸ +3KQ² (c₁§¿§¸ − ¤¸§₁ ) ( c₁₂ C₁₂ + § § ₁ ) - ȧ¸ = K@₁₂+r@₂ −3KQ² (c₁₂S₂¤¸ + §3§₁ ) c₁₂ Ó₁ = [(@c₂+w,s¸-rc₁)/c]-Q Ω Ò₂ = − (@₁ − 1 )§³ + @z€3 - 0₁ = {[a,c,-re, +0,5₁] s₂ / c₂} + w₂ (a) Derive the equation for ė₂
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