An axis-symmetric satellite is freely spinning in the space.

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SUMMARY

The discussion focuses on the dynamics of an axis-symmetric satellite freely spinning in space, specifically addressing the calculation of angular momentum and nutation frequency. Given the moments of inertia (Ix=200 kgm², Iy=Iz=100 kgm²) and initial angular velocities (wx=10 rad/sec, wy=1 rad/sec, wz=0), the angular momentum is calculated using Hx=Ixxwx, Hy=Iyywy, and Hz=Izzwz. The discussion also includes the need to utilize Euler angles for determining nutation frequency and visualizing the space and body cones.

PREREQUISITES
  • Understanding of angular momentum calculations in rigid body dynamics
  • Familiarity with moments of inertia for axis-symmetric bodies
  • Knowledge of Euler angles and their application in rotational motion
  • Concept of nutation frequency in the context of spinning bodies
NEXT STEPS
  • Calculate angular momentum for various configurations of rigid bodies
  • Explore the derivation of nutation frequency using Euler's equations
  • Study the visualization techniques for space and body cones in rotational dynamics
  • Investigate the effects of varying moments of inertia on satellite stability
USEFUL FOR

Aerospace engineers, physics students, and anyone studying the dynamics of rotating bodies in space will benefit from this discussion.

max1546
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Homework Statement


An axis-symmetric satellite is freely spinning in the space. The moments of inertia and the angular velocity at t=0 are as follows:
Ix=200kgm2
Iy=Iz=100kgm2
wx=10rad/sec
wy=1rad/sec
wz=0
(a) Calculate the angular momentum of the satellite
(b) What is the nutation frequency observed in the body-fixed frame?
(c) Sketch the space cone and the body cone.
(d) Calculate the time required for the body cone to make a revolution around the space cone.


Homework Equations





The Attempt at a Solution


ƩM=ΩχH
Hx=Ixxwx
Hy=Iyywy
Hz=Izzwz
I am not sure about how to deal with nutation frequency and the space/body cones
 
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Try using the euler angles.
 

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