What are the effects of Gravitomagnetism?

[Vorde]

I have been trying to understand what the effects of Gravitomagnetism are, I've looked at the equations, but my mathematical knowledge isn't high enough to be able to draw anything conclusive from them directly.

I've heard it both described as causing an attractive force (a la Magnetism), and I've also heard it described that when an object rotates, it causes objects around it to rotate as well.

Now to me it seems like those two things are not directly compatible, so if someone could clarify to me what it's exactly effects are it would be greatly appreciated.

Thank you.

 

[jfy4]

I think you can just consider the magnetic equations from Maxwell's equations, and that the situation is extremely analogous, including the "lorentz force law" for gravity.
$$\vec{\nabla}\times \vec{B}_g =-\vec{j}_g + \frac{\partial \vec{E}_{g}}{\partial t}$$
$$\vec{\nabla}\cdot \vec{B}_g=0$$
$$\vec{F}_g=m(\vec{E}_g+\vec{v}\times \vec{B}_g)$$