# [Orbital mechanics] Asteroid angular momentum

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1. Jan 7, 2016

### Jose Confraria

1. The problem statement, all variables and given/known data:
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?

2. Relevant equations
$$H_{i}=I_{ij}w_j$$

3. The attempt at a solution
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: Jan 7, 2016
2. Jan 7, 2016

### Tiago Valentim

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. Jan 7, 2016

### Jose Confraria

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.