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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 Assume that the body moves in a circular orbit at a constant rate Q. Let â be orbit-fixed unit vectors where a2 is directed from the orbit center to B*; then a3 is 90° from a₂ in the direction of motion and â₁ is parallel to the orbit normal. The dependent variables in the differential equations that govern motion include the measure numbers @₁; the kinematic variables that are the body 1-3-2 angles for orientation of C in A: w₁ = 0 - ȧ₂ = −K@₁w¸−r@¸ + 3KQ² (c₁₂§³ − c₁₁ ) (c₁₁₁ + S₁₁ ) - w₁ = Kw₁₂+rw₂ −3KQ² (c₁₂¤² + §3§₁ ) c₁₂ Ò₁ = [(@₁c³ + @¸§¸ − rc³)/2]-Q - Ò₁₂ = − (@₁ − r )s³ + @₁Cz • = {[−r¢+ ]s, /c,}+, Assume that the equations are numerically integrated using a spin rate of n=-4. At the instant when v=1.5 revs, the output is given as α = -4.000 02.0492 O₁ = 1.73° 0₂ = 4.50° 03.056 0₁ = 7.21° Let the precession angle relative to the orbit frame be 77 and the precession angle relative to the inertial frame be 5. Justify the relationship between 1 and 5. Determine the values for 7 and 5.

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 Assume that the body moves in a circular orbit at a constant rate Q. Let â be orbit-fixed unit vectors where a2 is directed from the orbit center to B*; then a3 is 90° from a₂ in the direction of motion and â₁ is parallel to the orbit normal. The dependent variables in the differential equations that govern motion include the measure numbers @₁; the kinematic variables that are the body 1-3-2 angles for orientation of C in A: w₁ = 0 - ȧ₂ = −K@₁w¸−r@¸ + 3KQ² (c₁₂§³ − c₁₁ ) (c₁₁₁ + S₁₁ ) - w₁ = Kw₁₂+rw₂ −3KQ² (c₁₂¤² + §3§₁ ) c₁₂ Ò₁ = [(@₁c³ + @¸§¸ − rc³)/2]-Q - Ò₁₂ = − (@₁ − r )s³ + @₁Cz • = {[−r¢+ ]s, /c,}+, Assume that the equations are numerically integrated using a spin rate of n=-4. At the instant when v=1.5 revs, the output is given as α = -4.000 02.0492 O₁ = 1.73° 0₂ = 4.50° 03.056 0₁ = 7.21° Let the precession angle relative to the orbit frame be 77 and the precession angle relative to the inertial frame be 5. Justify the relationship between 1 and 5. Determine the values for 7 and 5.

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
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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
Assume that the body moves in a circular orbit at a constant rate Q. Let â be orbit-fixed unit vectors where a2 is directed from the orbit center to B*; then a3 is 90° from a₂ in the direction of motion and â₁ is parallel to the orbit normal. The dependent variables in the differential equations that govern motion include the measure numbers @₁; the kinematic variables that are the body 1-3-2 angles for orientation of C in A: w₁ = 0 - ȧ₂ = −K@₁w¸−r@¸ + 3KQ² (c₁₂§³ − c₁₁ ) (c₁₁₁ + S₁₁ ) - w₁ = Kw₁₂+rw₂ −3KQ² (c₁₂¤² + §3§₁ ) c₁₂ Ò₁ = [(@₁c³ + @¸§¸ − rc³)/2]-Q - Ò₁₂ = − (@₁ − r )s³ + @₁Cz • = {[−r¢+ ]s, /c,}+, Assume that the equations are numerically integrated using a spin rate of n=-4. At the instant when v=1.5 revs, the output is given as α = -4.000 02.0492 O₁ = 1.73° 0₂ = 4.50° 03.056 0₁ = 7.21° Let the precession angle relative to the orbit frame be 77 and the precession angle relative to the inertial frame be 5. Justify the relationship between 1 and 5. Determine the values for 7 and 5.
Transcribed Image Text:Assume that the body moves in a circular orbit at a constant rate Q. Let â be orbit-fixed unit vectors where a2 is directed from the orbit center to B*; then a3 is 90° from a₂ in the direction of motion and â₁ is parallel to the orbit normal. The dependent variables in the differential equations that govern motion include the measure numbers @₁; the kinematic variables that are the body 1-3-2 angles for orientation of C in A: w₁ = 0 - ȧ₂ = −K@₁w¸−r@¸ + 3KQ² (c₁₂§³ − c₁₁ ) (c₁₁₁ + S₁₁ ) - w₁ = Kw₁₂+rw₂ −3KQ² (c₁₂¤² + §3§₁ ) c₁₂ Ò₁ = [(@₁c³ + @¸§¸ − rc³)/2]-Q - Ò₁₂ = − (@₁ − r )s³ + @₁Cz • = {[−r¢+ ]s, /c,}+, Assume that the equations are numerically integrated using a spin rate of n=-4. At the instant when v=1.5 revs, the output is given as α = -4.000 02.0492 O₁ = 1.73° 0₂ = 4.50° 03.056 0₁ = 7.21° Let the precession angle relative to the orbit frame be 77 and the precession angle relative to the inertial frame be 5. Justify the relationship between 1 and 5. Determine the values for 7 and 5.
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