Half

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15 years, 64 days

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These are answers submitted by Half

Energy: (For copy-paste) E[i] := VectorCalculus[`*`](VectorCalculus[`*`](1/2, l[s]), K[s](VectorCalculus[`+`](VectorCalculus[`*`](1/l[s], sqrt(DotProduct(VectorCalculus[`+`](`<,>`(x[VectorCalculus[`+`](i, 1)], y[VectorCalculus[`+`](i, 1)], z[VectorCalculus[`+`](i, 1)]), VectorCalculus[`-`](`<,>`(x[i], y[i], z[i]))), VectorCalculus[`+`](`<,>`(x[VectorCalculus[`+`](i, 1)], y[VectorCalculus[`+`](i, 1)], z[VectorCalculus[`+`](i, 1)]), VectorCalculus[`-`](`<,>`(x[i], y[i], z[i])))))), VectorCalculus[`-`](1)))^2) Derived force: F[x] := diff(VectorCalculus[`*`](VectorCalculus[`*`](1/2, l[s]), K[s](VectorCalculus[`+`](VectorCalculus[`*`](1/l[s], sqrt(DotProduct(VectorCalculus[`+`](`<,>`(x[VectorCalculus[`+`](i, 1)], y[VectorCalculus[`+`](i, 1)], z[VectorCalculus[`+`](i, 1)]), VectorCalculus[`-`](`<,>`(x[i], y[i], z[i]))), VectorCalculus[`+`](`<,>`(x[VectorCalculus[`+`](i, 1)], y[VectorCalculus[`+`](i, 1)], z[VectorCalculus[`+`](i, 1)]), VectorCalculus[`-`](`<,>`(x[i], y[i], z[i])))))), VectorCalculus[`-`](1)))^2), x[i])
I have tried performing the differentiation like you say, even before I went to these forums. I didn't quite like the results though. The derived expression, besides being very complex, contains D(Ks), which to my understanding would yield D(Ks) = 0 (Since Ks is a constant), in which case the entire expressions would reduce to: F(x[i],y[i],z[i]) = [0, 0, 0]. (Which is certainly incorrect in the general case) Maybe the problem is that l[i] and Ks are not defined as constants in my worksheet.. Do I need to do that, and how?
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