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Y, Y The 200kg satellite shown above is initially at an orientation of (roll, pitch, yaw) (0) = (0,0,0)° and has an angular velocity vector w = 100i + 10j deg/s, in body-fixed reference coordinates as shown (at the satellite's centre of mass). The satellite has rotational symmetry about its x-axis (hence symmetry about the x-z plane and x-y plane) and its shape can be approximated as a box with side lengths of 1.0m in the y and z directions, and a side length of 3m in the x direction. i) Compute the mass moments of inertia, products of inertia and form the inertia matrix for the satellite, approximating as a box, using the x-y-z body axes shown, located at the center of the box. Provide answers in kg.m2 and using two decimal places: XX = xy = , lyy= Angular Momentum HG = $22 Z, z , lyz = Angle between HG and w= ii) Compute the angular momentum vector for the satellite about the mass center, and compute the angle between the angular momentum vector and angular velocity vector: k kg.m²/s (provide answer using one decimal place) , Izz = i+ , Izx= j+ degrees (provide answer using 2 decimal places) iii) Compute the rates of change of the body-fixed angular velocity vector components of the satellite at this point in time:

Y, Y The 200kg satellite shown above is initially at an orientation of (roll, pitch, yaw) (0) = (0,0,0)° and has an angular velocity vector w = 100i + 10j deg/s, in body-fixed reference coordinates as shown (at the satellite's centre of mass). The satellite has rotational symmetry about its x-axis (hence symmetry about the x-z plane and x-y plane) and its shape can be approximated as a box with side lengths of 1.0m in the y and z directions, and a side length of 3m in the x direction. i) Compute the mass moments of inertia, products of inertia and form the inertia matrix for the satellite, approximating as a box, using the x-y-z body axes shown, located at the center of the box. Provide answers in kg.m2 and using two decimal places: XX = xy = , lyy= Angular Momentum HG = $22 Z, z , lyz = Angle between HG and w= ii) Compute the angular momentum vector for the satellite about the mass center, and compute the angle between the angular momentum vector and angular velocity vector: k kg.m²/s (provide answer using one decimal place) , Izz = i+ , Izx= j+ degrees (provide answer using 2 decimal places) iii) Compute the rates of change of the body-fixed angular velocity vector components of the satellite at this point in time:

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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Y, Y Ixx = Ixy = The 200kg satellite shown above is initially at an orientation of (roll, pitch, yaw) (0) = (0,0,0)° and has an angular velocity vector w = 100i + 10j deg/s, in body-fixed reference coordinates as shown (at the satellite's centre of mass). The satellite has rotational symmetry about its x-axis (hence symmetry about the x-z plane and x-y plane) and its shape can be approximated as a box with side lengths of 1.0m in the y and z directions, and a side length of 3m in the x direction. Angular Momentum HG = (i) Compute the mass moments of inertia, products of inertia and form the inertia matrix for the satellite, approximating as a box, using the x-y-z body axes shown, located at the center of the box. Provide answers in kg.m² and using two decimal places: , lyy = Angle between HG and w= = ملت lyz = =ولنا = لنا Z, Z (ii) Compute the angular momentum vector for the satellite about the mass center, and compute the angle between the angular momentum vector and angular velocity vector: k kg.m²/s (provide answer using one decimal place) rad/s2 rad/s2 Izz = i+ X, X Izx = 1m j+ (iii) Compute the rates of change of the body-fixed angular velocity vector components of the satellite at this point in time: rad/s2 1m 3m degrees (provide answer using 2 decimal places) Provide answers using two decimal places. (iv) Use the 3D torque-free motion demo (which is located on the course Canvas site under Modules/week 10) to simulate the behaviour of the satellite's motion. See if you can explain the motion observed and why this occurs, even when there are no external moments acting on the satellite (no marks for this part of the question).
Transcribed Image Text:Y, Y Ixx = Ixy = The 200kg satellite shown above is initially at an orientation of (roll, pitch, yaw) (0) = (0,0,0)° and has an angular velocity vector w = 100i + 10j deg/s, in body-fixed reference coordinates as shown (at the satellite's centre of mass). The satellite has rotational symmetry about its x-axis (hence symmetry about the x-z plane and x-y plane) and its shape can be approximated as a box with side lengths of 1.0m in the y and z directions, and a side length of 3m in the x direction. Angular Momentum HG = (i) Compute the mass moments of inertia, products of inertia and form the inertia matrix for the satellite, approximating as a box, using the x-y-z body axes shown, located at the center of the box. Provide answers in kg.m² and using two decimal places: , lyy = Angle between HG and w= = ملت lyz = =ولنا = لنا Z, Z (ii) Compute the angular momentum vector for the satellite about the mass center, and compute the angle between the angular momentum vector and angular velocity vector: k kg.m²/s (provide answer using one decimal place) rad/s2 rad/s2 Izz = i+ X, X Izx = 1m j+ (iii) Compute the rates of change of the body-fixed angular velocity vector components of the satellite at this point in time: rad/s2 1m 3m degrees (provide answer using 2 decimal places) Provide answers using two decimal places. (iv) Use the 3D torque-free motion demo (which is located on the course Canvas site under Modules/week 10) to simulate the behaviour of the satellite's motion. See if you can explain the motion observed and why this occurs, even when there are no external moments acting on the satellite (no marks for this part of the question).
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