I tried to find the differental equations that describe geodesics in polar coordinates.(adsbygoogle = window.adsbygoogle || []).push({});

Using [tex]g=\left[\begin{matrix} 1 & 0 \\ 0 & r^2 \end{matrix}\right][/tex] as the metric.

I did not show the steps in expanding the Christoffel symbol. There are three nonzero elements in it, simplified there are two elements (Two of the three are equal).

http://img686.imageshack.us/img686/1561/geodesic.jpg [Broken]

Where the two cases [tex]\lambda=1,2[/tex] have to hold simultaneously.

The differential equations I found here say that any path going radially outwards from the center in a geodesic, which is expected. Also, circles are not geodesics.

I guess that the only way to test the validity of the equations is to plug in a general expresssion for a straight line?

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Geodesic equations

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

Loading...

Similar Threads - Geodesic equations | Date |
---|---|

I Deduce Geodesics equation from Euler equations | Dec 7, 2017 |

I Example of computing geodesics with 2D polar coordinates | Aug 6, 2016 |

How do I use the geodesic equation for locations on earth | Dec 19, 2015 |

Geodesic deviation equation | May 24, 2015 |

Geodesic equations and Christoffel symbols | May 2, 2014 |

**Physics Forums - The Fusion of Science and Community**