How Many Additive Integrals of Motion Exist in a Closed Mechanical System?

[S.P.P]

Hi all,

Was given a question which went like this:

Consider a closed mechanical system described by s generalized coordinates qi. How many additive integrals of motions exist for this system?

I'm not quite sure exactly what is meant by this. I know that there are 2s-1 integrals for this closed system, but how do I go about finding out how many additive integrals there are. I also know that there are 7 additive integrals important to classical mechanics, energy, and the 3 components of momentum, and 3 of angular momentum. So is the answer just 7, or is there something I've missed?

Thanks for any help

 

[S.P.P]

That should read:

'I know that there are 2s-1 independent integrals for this closed system'