# [Orbital mechanics] Asteroid angular momentum

## 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?

## Homework Equations

$$H_{i}=I_{ij}w_j$$

## 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

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