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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}) \\ 
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 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)