equations:geodesic_equation
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equations:geodesic_equation [2018/05/04 09:53] jakobadmin ↷ Links adapted because of a move operation |
equations:geodesic_equation [2018/12/19 11:01] (current) jakobadmin ↷ Links adapted because of a move operation |
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| &= m\sqrt{g_{ij}\dot{q}^i\dot{q}^j} | &= m\sqrt{g_{ij}\dot{q}^i\dot{q}^j} | ||
| \end{align*} | \end{align*} | ||
| - | just like in [[theories:special_relativity|special relativity]] but instead of the [[advanced_tools:minkowski_metric|Minkowski metric]] $\eta_{ij}$, we now have a general metric $g_{ij}$. Alternatively we can use | + | just like in [[models:special_relativity|special relativity]] but instead of the [[advanced_tools:minkowski_metric|Minkowski metric]] $\eta_{ij}$, we now have a general metric $g_{ij}$. Alternatively we can use |
| \begin{align*} | \begin{align*} | ||
| L(q,\dot{q}) &= \tfrac{1}{2}m g(q)(\dot{q},\dot{q}) \\ | L(q,\dot{q}) &= \tfrac{1}{2}m g(q)(\dot{q},\dot{q}) \\ | ||
| Line 73: | Line 73: | ||
| In the geometric optics approximation light acts like particles tracing out geodesics, i.e. the shortest paths. | In the geometric optics approximation light acts like particles tracing out geodesics, i.e. the shortest paths. | ||
| - | Especially in [[theories:general_relativity|general relativity]] particles always follow geodesics. To be precise, a free particle in general relativity traces out a geodesic on the Lorentzian manifold, i.e. spacetime. | + | Especially in [[models:general_relativity|general relativity]] particles always follow geodesics. To be precise, a free particle in general relativity traces out a geodesic on the Lorentzian manifold, i.e. spacetime. |
equations/geodesic_equation.1525420401.txt.gz · Last modified: 2018/05/04 07:53 (external edit)
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