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Assuming no external torque or forces acting can a rigid body be set in perpetual rotation motion about an axis which is not its principal axis?
If no then does the earth continuously change its axis of rotation? as the principal axes of the earth changes changes continuously because of tectonic plate movements, animals humans moving etc.
The answer to your first question is no, any rotation about a non-principal axis will result in the axis of rotation changing. To see why, lets go into the body frame of the object, where with no torques the angular momentum follows the equation
$$\mathbf{\dot{L}}+\boldsymbol{ \omega} \times \mathbf{L=0}$$
Where $\mathbf{L}$ is the angular momentum of the system and $\boldsymbol{ \omega}$ is the axis of rotation. Now, $\mathbf{L}=I\boldsymbol{ \omega}$, where $I$ is the moment of inertia tensor. By definition, a principal axis is an eigenvector of the moment of intertia, so if $\boldsymbol{ \omega}$ is not along a principal axis, $\mathbf{L}$ can't be pointing in the same direction as $\boldsymbol{ \omega}$. In our body frame of reference, $\dot{I}=0$. Differentiating our previous expression for $\mathbf{L}$ and combining with our first equation, we have
$$I\boldsymbol{\dot{\omega}}+\boldsymbol{ \omega} \times \mathbf{L=0}$$
Now, a stationary axis of roation requires that within the body frame of reference, $\boldsymbol{\dot{\omega}=0}$. But from our equation above, this leaves us with the requirement that $\boldsymbol{ \omega} \times \mathbf{L=0}$. The cross product of two non-zero vectors is only zero if they are parallel, which we already ruled out by virtue of choosing a non-principal axis of rotation. Thus, it is impossible to have steady rotation about a non-principal axis.
As to your second question, the Earth's axis does indeed change over time, although this is mainly because of torques exerted on the Earth due to gravitational interactions. The Earth is close enough to being spherical that every axis is very nearly a principal one, so the precession of the axis caused by obliquity of the Earth is rather negligible.
Assuming no external torque or forces acting can a rigid body be set in perpetual rotation motion about an axis which is not its principal axis?
In a nutshell? No.
If a body rotates about a principal axis (an axis through its centre of mass) and no external torques act on it, then it will forever keep rotating.
Now look at the case where the rotation in NOT about a principal axis:
In order to keep the rotation going, a force has to act on it, called the centripetal force, $F_c$. It's a vector pointing from the centre of mass of the object to the axis of rotation.
In vector notation we can write:
$$\mathrm{F_c}=-m\omega^2\mathbf{r}$$
where $m$ is the object's mass, $r$ the radius of the orbit and $\omega$ its angular velocity.
If this force ceases to act then the object will leave its orbital trajectory.
If no then does the earth continuously change its axis of rotation? as the principal axes of the earth changes changes continuously because of tectonic plate movements, animals humans moving etc.
It doesn't really. The effects you list are minimal, compared to the inertial moment/inertial momentum of the Earth.
