• Support PF! Buy your school textbooks, materials and every day products Here!

[Orbital mechanics] Asteroid angular momentum

  • #1

Homework Statement

: [/B]
A vector is perpendicular to B vector, and they stay still, relative to the body. No torque is applied on the asteroid, although he dissipates very little rotational kinetic energy, due to drag on dust clouds. It was also determined that the asteroid is a long body axisymmetric from inercia's point of view. In a certain instant, lets call it t1, the body was rotating in A axis with angular velocity w1 = 2 rad/s. In another instant, t2 ( 1 and 2 are not related to which time is first) we see that apparently the asteroid is rotating on B axis with angular velocity w2=3 rad/s. Knowing that the angular momentum of the asteroid relative to the center of mass is constant H0=10^10 kg.m^2/s and was kept constant between both instants and that the time between them is very large, calculate the inertial tensor on the principal axis. And which time came first, t2 or t1?
IH84A1P.png


Homework Equations


[tex]H_{i}=I_{ij}w_j[/tex]
2CjqNl2.png

The Attempt at a Solution


I have already tryed anything i can remember. Been on more than 3 hours thinking about this exercise.
Although, i think i don't even know where to start. d/dt H is 0 as there is no torque applied on the asteroid. But after that what do i know? A and B are not on the pricipal axis.
I am just completely stuck in this exercise like something is missing.

Precession is constant => psi=H/A. on principal axis
Nutation angle is constant
 
Last edited:

Answers and Replies

  • #2
Hmmmm given the way that the problem is written, they are the principal axis (see the indication that one instant is very far apart from the other giving some clue about stability and equilibrium). Try doing it now!
 
  • #3
I also agree with you. There is no other way this can have a solution, but if that's the case it is very simple. Oh well i guess this is answered.
 

Related Threads for: [Orbital mechanics] Asteroid angular momentum

  • Last Post
Replies
1
Views
4K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
0
Views
1K
Replies
2
Views
1K
Replies
5
Views
1K
Replies
4
Views
1K
  • Last Post
Replies
4
Views
4K
Replies
3
Views
1K
Top