equations:geodesic_equation
| Both sides previous revision Previous revision Next revision | Previous revision | ||
|
equations:geodesic_equation [2018/04/14 11:22] aresmarrero ↷ Links adapted because of a move operation |
equations:geodesic_equation [2018/12/19 11:01] (current) jakobadmin ↷ Links adapted because of a move operation |
||
|---|---|---|---|
| Line 7: | Line 7: | ||
| Geodesics are the "shortest" paths between two points in a flat spacetime and the straightest path between two points in a curved spacetime. | Geodesics are the "shortest" paths between two points in a flat spacetime and the straightest path between two points in a curved spacetime. | ||
| | | ||
| + | On a sphere the geodesics are "great circles". | ||
| <tabbox Concrete> | <tabbox Concrete> | ||
| Line 48: | Line 49: | ||
| \end{align*} | \end{align*} | ||
| where the last line follows since $g_{ik}=g_{ki}$. | where the last line follows since $g_{ik}=g_{ki}$. | ||
| - | Now we define the so-called [[advanced_tools:connections:christoffel_symbols|Christoffel symbols]] | + | Now we define the so-called [[advanced_tools:connections:levi_civita_connection|Christoffel symbols]] |
| \[ | \[ | ||
| \Gamma_{ijk} \equiv -\bigl(\partial_{i}g_{jk}-\partial_{k}g_{ij}-\partial_{j}g_{ki}\bigr) | \Gamma_{ijk} \equiv -\bigl(\partial_{i}g_{jk}-\partial_{k}g_{ij}-\partial_{j}g_{ki}\bigr) | ||
equations/geodesic_equation.1523697739.txt.gz · Last modified: 2018/04/14 09:22 (external edit)
Page Tools
Except where otherwise noted, content on this wiki is licensed under the following license: CC Attribution-Share Alike 4.0 International
