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I was looking over my notes for centre of mass for a system and it says:

[tex] c = \frac {1} {M} \sum_{i} m_i\ddot{r}_i = \sum_{i}(E_i + \sum_{j \neq i}F_i_j) [/tex]

where M is the total mass of the system.

Then it considers the centre of Mass in motion:

[tex] M \ddot{c} = \sum_i m_i \ddot{r}_i = \sum_{i}(E_i + \sum_{j \neq i}F_i_j) [/tex]

[tex] = \sum_{i}E_i + \sum_{j \neq i}F_i_j = E + \sum_{i < j}(F_j_i + F_j_j)[/tex]

[tex] = E [/tex]

The thing is, I don't understand the line:

[tex]E + \sum_{i < j}(F_j_i + F_j_j)[/tex]

and how it comes about (especially the i < j) part.

Any help would be grateful!

[tex] c = \frac {1} {M} \sum_{i} m_i\ddot{r}_i = \sum_{i}(E_i + \sum_{j \neq i}F_i_j) [/tex]

where M is the total mass of the system.

Then it considers the centre of Mass in motion:

[tex] M \ddot{c} = \sum_i m_i \ddot{r}_i = \sum_{i}(E_i + \sum_{j \neq i}F_i_j) [/tex]

[tex] = \sum_{i}E_i + \sum_{j \neq i}F_i_j = E + \sum_{i < j}(F_j_i + F_j_j)[/tex]

[tex] = E [/tex]

The thing is, I don't understand the line:

[tex]E + \sum_{i < j}(F_j_i + F_j_j)[/tex]

and how it comes about (especially the i < j) part.

Any help would be grateful!

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