Dear Everyone:

I am studying a rigid body motion in n-dimensional Euclidean space.

My focus is on rigid bodies which merely consist of some m points in n-dim space.

In 3-dim spaces, only translations and rotations exist for rigid body motion.

May I ask:

I want to know the types of movements of rigid body in n-dim spaces.

Are translations and rotations all I need to consider? Or Do there any other types of movements(transformations) exist?

In n-dim spaces, if translations and rotations are all I need to consider,

what is the general formulae for rotations in n-dim ?

Also, I will really appreciate if you could recommend me good websites or books etc to study such topics.

Thank you and have a nice day, all of you