Analyzing a perfect physical sphere in space I see it having two kinds of movements, one will be defining the center position of the sphere in 3D space with a velocity that will not change unless there is a force, and the other is the rotation of the sphere, this is the part that i still dont fully understand.

What i think is that this rotation will have 3 axis and like the translation has a velocity that doent change without a force, the sphere will have too a velocity of rotation defined in those three axis that doesnt change unless there is a force.

After seeing how the earth moves around the sun I can say that a perfect sphere in space is not limited to rotate around a fixed axis.

Can I describe all possible ways a sphere can rotate (forever unless there is a force) defining a velocity in those 3 axis?

You are talking about torque, and yes, 3 axis are more than enough, in fact, every possible rotation in 3d can be described as a rotation around a single vector (axis). This is very helpful, because you can compress a rotation into a vector and an angle. The mathematically construct of this is called quaternion.

No, he is talking about angular velocity, which is not a rotation, but a pseudo-vector, and that pseudo-vector is three-dimensional. (For the more mathematically savvy people in the forum: Rotations form a Lie group and angular velocity is an element of the corresponding Lie algebra.)

I think the answer the OP is looking for is that position, velocity, attitude (that one is a rotation) and angular velocity are enough to describe the state of a solid object in mechanics, as he initially thought. Whatever extra things the Earth does have to do with external forces.

After seeing how the earth moves around the sun I can say that a perfect sphere in space is not limited to rotate around a fixed axis.

The Earth is not a perfect sphere, nor is it a perfectly rigid body with uniform density, or any of that. It sounds like you want math more suited to billiard balls, not planets.

The earth example was to show that a fixed axis of rotation isnt enought to descibe all kinds of that rotation that can go forever on a sphere in space, in the earth example it is rotating around an axis and the axis is rotationg around another axis (and i think that axis movement is forever).

Can I describe that rotational movement that can go forever in asphere with a magnitude in those fixed 3 axis(image)?

Perhaps my earlier answer wasn't clear enough: In the absence of external forces, the angular velocity is all you need to describe how an object rotates forever. The Earth does all sorts of funny things because there are external forces. See this Wikipedia page for details.

in the earth example the axis is moving too

Moving in relation to what? You need a frame of reference to define motion, both translation and rotation.

I am not sure that's true. At least in Newtonian mechanics, there is a notion of an inertial frame of reference, and rotations are the same under all inertial frames of reference.

so the axis "rotating" aroung another axis is because the earth isnt a perfect sphere, ok i undestand it now, the precessin of the erath was making me think a perfect sphere could move in rare ways.

so the axis "rotating" aroung another axis is because the earth isnt a perfect sphere, ok i undestand it now, the precessin of the erath was making me think a perfect sphere could move in rare ways.

No, it's because there are external forces acting on Earth. Read the Wikipedia page I linked to earlier.