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* Page found: Trägheitstensor (eq math.1138.5)

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T=\frac{1}{2}\sum\limits_{i=1}^{N}{{{m}_{i}}{{\left( {{{\dot{r}}}_{0}}+\left( \omega \times {{r}_{i}} \right) \right)}^{2}}}=\frac{1}{2}M{{\dot{r}}_{0}}^{2}+\sum\limits_{i=1}^{N}{{{m}_{i}}{{{\dot{r}}}_{0}}\centerdot \left( \omega \times {{r}_{i}} \right)}+\frac{1}{2}\sum\limits_{i=1}^{N}{{{m}_{i}}{{\left( \omega \times {{r}_{i}} \right)}^{2}}}

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T = 1 2 ⁢ ∑ i = 1 N m i ⁢ ( r ˙ 0 + ( ω × r i ) ) 2 = 1 2 ⁢ M ⁢ r ˙ 0 2 + ∑ i = 1 N m i ⁢ r ˙ 0 ∙ ( ω × r i ) + 1 2 ⁢ ∑ i = 1 N m i ⁢ ( ω × r i ) 2 𝑇 1 2 superscript subscript 𝑖 1 𝑁 subscript 𝑚 𝑖 superscript subscript ˙ 𝑟 0 𝜔 subscript 𝑟 𝑖 2 1 2 𝑀 superscript subscript ˙ 𝑟 0 2 superscript subscript 𝑖 1 𝑁 ∙ subscript 𝑚 𝑖 subscript ˙ 𝑟 0 𝜔 subscript 𝑟 𝑖 1 2 superscript subscript 𝑖 1 𝑁 subscript 𝑚 𝑖 superscript 𝜔 subscript 𝑟 𝑖 2 {\displaystyle{\displaystyle T=\frac{1}{2}\sum\limits_{i=1}^{N}{{{m}_{i}}{{% \left({{{\dot{r}}}_{0}}+\left(\omega\times{{r}_{i}}\right)\right)}^{2}}}=\frac% {1}{2}M{{\dot{r}}_{0}}^{2}+\sum\limits_{i=1}^{N}{{{m}_{i}}{{{\dot{r}}}_{0}}% \centerdot\left(\omega\times{{r}_{i}}\right)}+\frac{1}{2}\sum\limits_{i=1}^{N}% {{{m}_{i}}{{\left(\omega\times{{r}_{i}}\right)}^{2}}}}}

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T=12∑i=1Nmi(r˙0+(ω×ri))2=12Mr˙02+∑i=1Nmir˙0⋅(ω×ri)+12∑i=1Nmi(ω×ri)2

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