Quote:Original post by arithma
The formula that I posted is the reverse of what I needed [grin]
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pi(ri) = ri-2 L cross ri
No, that is most definitely p given r under the constraints you required, which is what you asked for. What's the revese? The inverse (r given p)? But r_i(p_i) isn't well-defined. You already have L_i in terms of r_i and p_i. What do you want?
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I drop any relevancy issues that were raised in face of using orbits. However I praise the avoidance of their usage in the discussion. After all we are trying to figure out an intuitive sense around angular momentum [smile].
It sounds like you already have an intuitive sense. The very fact that you say "Not all p_i = 0" and "Sum({p_i}) = 0" implies "Spinning" shows this.
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Now let's get down to the dirt.
I'm not sure it can be done. Eventually, you're just going to have to pull that (r x p) out of your ass and comment that it doesn't change given the constraints. My recommendation: Try it with just two particles and note that it can be extended to more discrete particles and continuous bodies. Cylindrical coordinates can help.
If you don't want to just pull it out of your ass, you're not going to get there by your route.