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two-body_problem [2014/03/21 11:11] 127.0.0.1 external edit |
two-body_problem [2015/08/19 19:50] (current) nikolaj |
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| ==== Set ==== | ==== Set ==== | ||
| | @#FFBB00: definiendum | @#FFBB00: $\langle \mathbb R^{2\times 3}, H\rangle \in \mathrm{it} $ ... Classical Hamiltonian system | | | @#FFBB00: definiendum | @#FFBB00: $\langle \mathbb R^{2\times 3}, H\rangle \in \mathrm{it} $ ... Classical Hamiltonian system | | ||
| - | |||
| | @#55EE55: postulate | @#55EE55: $ H({\bf r}_1,{\bf r}_2,{\bf p}_1,{\bf p}_2) = \frac{1}{m_1}\frac{1}{2}{\bf p}_1^2 + \frac{1}{m_2}\frac{1}{2}{\bf p}_2^2 + V(|{\bf r}_1-{\bf r}_2|) $ | | | @#55EE55: postulate | @#55EE55: $ H({\bf r}_1,{\bf r}_2,{\bf p}_1,{\bf p}_2) = \frac{1}{m_1}\frac{1}{2}{\bf p}_1^2 + \frac{1}{m_2}\frac{1}{2}{\bf p}_2^2 + V(|{\bf r}_1-{\bf r}_2|) $ | | ||
| - | ==== Discussion ==== | + | ----- |
| + | === Discussion === | ||
| == Equations of motion in suitable coordinates == | == Equations of motion in suitable coordinates == | ||
| | @#DDDDDD: range | @#DDDDDD: $ M \equiv m_1+m_2 $ | | | @#DDDDDD: range | @#DDDDDD: $ M \equiv m_1+m_2 $ | | ||
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| [[http://en.wikipedia.org/wiki/Two-body_problem|Two-body problem]], [[http://en.wikipedia.org/wiki/Rutherford_scattering|Rutherford scattering]], [[http://en.wikipedia.org/wiki/Impact_parameter|Impact parameter]] | [[http://en.wikipedia.org/wiki/Two-body_problem|Two-body problem]], [[http://en.wikipedia.org/wiki/Rutherford_scattering|Rutherford scattering]], [[http://en.wikipedia.org/wiki/Impact_parameter|Impact parameter]] | ||
| - | ==== Parents ==== | + | ----- |
| === Subset of === | === Subset of === | ||
| [[Classical Hamiltonian system]] | [[Classical Hamiltonian system]] | ||
