Given a spacecraft with the following principle moments of inertia: [1500 0 0 J = cos(8) 0 1500 0 a) Assuming torque free motion, calculate the minimum rotational velocity n that will keep the nutation angle below 1.0 degree, if the transverse rotational velocity @12 = 0.05 deg/s. (Be careful of units) 0 0 2500 J3n √(W₁2)² + √√√3n)² or tan(0) = b) MATLAB-Given the closed form solutions of the torque free differential equations of motion, use MATLAB to plot how changes over a time period starting at t = 0 seconds to t = 1000 seconds. Use the initial conditions n = 2.0 deg/s, w₁(0) = 0.1 deg/s, w2(0) = 0.6 deg/s. Use the MATLAB function subplot() to create three plots on the same figure for each element of w. w₁(t) = w₁(0) cos(at) + w₂ (0) sin(at) w₂ (t) = w₂(0) cos(at) - w₁(0) sin(at) w3(t) = n Jw12 J3n c) MATLAB - Given the same initial conditions and time period as part (b) and the closed form solutions of the constant torque differential equations of motion, use MATLAB to plot how changes with a constant torque of M₁ = 20.0 Nm. Comment on the similarities and differences between the plots from part (b) and part (c). w₁(t) = w₁(0) cos(lt) + w₂(0) sin(at) + w₂(t) = w₂ (0) cos(lt) — w₁(0) sin(at) - w3(t) = n sin(at) (1 - cos(at))
Given a spacecraft with the following principle moments of inertia: [1500 0 0 J = cos(8) 0 1500 0 a) Assuming torque free motion, calculate the minimum rotational velocity n that will keep the nutation angle below 1.0 degree, if the transverse rotational velocity @12 = 0.05 deg/s. (Be careful of units) 0 0 2500 J3n √(W₁2)² + √√√3n)² or tan(0) = b) MATLAB-Given the closed form solutions of the torque free differential equations of motion, use MATLAB to plot how changes over a time period starting at t = 0 seconds to t = 1000 seconds. Use the initial conditions n = 2.0 deg/s, w₁(0) = 0.1 deg/s, w2(0) = 0.6 deg/s. Use the MATLAB function subplot() to create three plots on the same figure for each element of w. w₁(t) = w₁(0) cos(at) + w₂ (0) sin(at) w₂ (t) = w₂(0) cos(at) - w₁(0) sin(at) w3(t) = n Jw12 J3n c) MATLAB - Given the same initial conditions and time period as part (b) and the closed form solutions of the constant torque differential equations of motion, use MATLAB to plot how changes with a constant torque of M₁ = 20.0 Nm. Comment on the similarities and differences between the plots from part (b) and part (c). w₁(t) = w₁(0) cos(lt) + w₂(0) sin(at) + w₂(t) = w₂ (0) cos(lt) — w₁(0) sin(at) - w3(t) = n sin(at) (1 - cos(at))
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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![1) Given a spacecraft with the following principle moments of inertia:
[1500 0
1500
0
J= 0
0
cos(0) =
a) Assuming torque free motion, calculate the minimum rotational velocity n that will keep the nutation angle
below 1.0 degree, if the transverse rotational velocity @12 = 0.05 deg/s. (Be careful of units)
0
0
2500]
J3n
(W12)² + (√3)²
or tan(0) =
JW12
J3n
b) MATLAB - Given the closed form solutions of the torque free differential equations of motion, use MATLAB
to plot how changes over a time period starting at t = 0 seconds to t= 1000 seconds. Use the initial
conditions n = 2.0 deg/s, w₁(0) = 0.1 deg/s, w₂(0) = 0.6 deg/s. Use the MATLAB function subplot() to
create three plots on the same figure for each element of w.
w₁(t) = w₁(0) cos(at) + w₂(0) sin(at)
w₂ (t)=w₂ (0) cos(at) - w₁ (0) sin(at)
W3 (t) = n
c) MATLAB - Given the same initial conditions and time period as part (b) and the closed form solutions of the
constant torque differential equations of motion, use MATLAB to plot how a changes with a constant torque
of M₁ = 20.0 Nm. Comment on the similarities and differences between the plots from part (b) and part (c).
w₁(t) = w₁(0) cos(at) + w₂(0) sin(at) + +
sin(at)
μl
w₂ (t) = w₂ (0) cos(lt) — w₁(0) sin(lt) – (1 − cos(lt))
w3(t) = n](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5c85250b-6a52-47e3-86e8-89d741652c47%2F658b1622-0cc8-468e-a898-3279190f284f%2Fdzavodi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1) Given a spacecraft with the following principle moments of inertia:
[1500 0
1500
0
J= 0
0
cos(0) =
a) Assuming torque free motion, calculate the minimum rotational velocity n that will keep the nutation angle
below 1.0 degree, if the transverse rotational velocity @12 = 0.05 deg/s. (Be careful of units)
0
0
2500]
J3n
(W12)² + (√3)²
or tan(0) =
JW12
J3n
b) MATLAB - Given the closed form solutions of the torque free differential equations of motion, use MATLAB
to plot how changes over a time period starting at t = 0 seconds to t= 1000 seconds. Use the initial
conditions n = 2.0 deg/s, w₁(0) = 0.1 deg/s, w₂(0) = 0.6 deg/s. Use the MATLAB function subplot() to
create three plots on the same figure for each element of w.
w₁(t) = w₁(0) cos(at) + w₂(0) sin(at)
w₂ (t)=w₂ (0) cos(at) - w₁ (0) sin(at)
W3 (t) = n
c) MATLAB - Given the same initial conditions and time period as part (b) and the closed form solutions of the
constant torque differential equations of motion, use MATLAB to plot how a changes with a constant torque
of M₁ = 20.0 Nm. Comment on the similarities and differences between the plots from part (b) and part (c).
w₁(t) = w₁(0) cos(at) + w₂(0) sin(at) + +
sin(at)
μl
w₂ (t) = w₂ (0) cos(lt) — w₁(0) sin(lt) – (1 − cos(lt))
w3(t) = n
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