Question about "bound systems"

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Discussion Overview

The discussion revolves around the concept of "bound systems" in the context of particle dynamics, specifically focusing on the relationship between the center of mass (CM) motion and the degrees of freedom of the bound system. Participants explore whether the movement of the CM is linked to the internal degrees of freedom and the implications of energy transfer between them.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant questions whether the degree of freedom of the CM is linked to other degrees of freedom of the bound system.
  • Another participant asserts that, under certain general assumptions, the movement of the CM can be separated from the movement of the particles relative to the CM.
  • A follow-up inquiry seeks clarification on the specific assumptions that allow for this separation of motion.
  • A participant explains that the separation is possible if the potential energy can be split into components that depend on interparticle distances and the CM position, while noting that time-dependent interparticle potentials could lead to the system becoming unbound.
  • One participant challenges the explanation by suggesting it may be tautological, except for the detail regarding potential energy dependence on distance rather than its derivatives.

Areas of Agreement / Disagreement

There is no consensus on the explanation provided regarding the separation of CM motion from the internal degrees of freedom, as one participant challenges the reasoning presented.

Contextual Notes

The discussion includes assumptions about potential energy forms and external forces acting on particles, which may not be universally applicable. The implications of time-dependent potentials on system binding are also noted but remain unresolved.

ORF
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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.
 
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ORF said:
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.
 
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 :)
 
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).
 
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
 

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