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[itex]\left(\frac{dx(t)}{dt}\right)^2

= \frac{1}{N^2} c^2 \sum_{i\neq j} \left(1-\frac{v_i(t) v_j(t)}{c^2}\right) [/itex]

where the [itex]v_i[/itex] are the velocity vectors (3 dimensions) of the N points. They fulfil the equation [itex]|v_i(t)|^2 = c^2[/itex]. If I didn't loose some constant factor, the equation above should be the same as

[itex]\left(\frac{dx(t)}{dt}\right)^2

= \frac{1}{N^2} \sum_{i< j} (v_i - v_j)^2[/itex]

Any chance to solve one or the other for [itex]x(t)[/itex]? I hesitate to take the square root and try to integrate the square root of the sum. Are there better ways to solve this?

Harald.