equations:geodesic_equation

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equations:geodesic_equation [2018/05/05 22:00] jakobadmin [Concrete] |
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.txt · Last modified: 2018/12/19 11:01 by jakobadmin

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