Question about "bound systems"

[ORF]

Hello

If we have a system of several particles bound between them, we often separate the movement of CM from the degrees of freedom of the bound system.

Is the degree of freedom of the CM linked to other degrees of freedom of the bound system?
Equivalent questions: can we unbound (untie, unfasten, set free) the particles by giving* energy to the CM?, or vice versa, can we bound "stronger" by draining energy from the degrees of freedom to CM]?

*I don't know what verb is used instead of give; maybe "convey" would be a more specific word.

My mother language is not English, please forgive any mistake.

Thank you for your time :)

Greetings.

 

[Orodruin]

Is the degree of freedom of the CM linked to other degrees of freedom of the bound system?

No, for some quite general assumptions, you can separate the movement of the CM from the movement of the particles relative to the CM.

 

[ORF]

Hi!

Thank you for answering so quickly.

What assumptions allow separate the movement of the CM from the movement of the particles relative to the CM?

Greetings :)

 

[Orodruin]

Essentially it is sufficient that you can split the potential energy into two parts, one that only depends on the interparticle distances, and one that depends only on the CM position. Both may also depend on time, but the interparticle potential changing with time may lead to the system becoming unbound (but still describable separating the CM coordiantes).

This is equivalent to requiring that any external forces acts on each particle with a force proportional to its mass (i.e., giving each particle the same acceleration).

 

[ORF]

Hello

But... that is a tautology, isn't? [except for the detail of potential depending only on the distance and not on its derivatives]

Thank you for your time :)

Greetings