Why can't a three/more body problem be reduced to a one-body problem?

[neelakash]

We know a two body problem may be analysed as an equivalent one body problem.Why a three/more body problem cannot be reduced to a one-body problem?

I think in that case we do not find an equivalent reduced mass...
Anyone can say something?

 

[StatMechGuy]

Try to come up with a coordinate transformation that does any good. Relative coordinates don't work, you need three to specify everything. This is no better than the starting position. Just give it a shot and you'll see.

 

[Meir Achuz]

For three bodies, you can reduce the independent vectors to two plus the coordinate of the overall center of mass.