Hello,(adsbygoogle = window.adsbygoogle || []).push({});

I'm beginning to learn GR and ran across the following in the beginning of Stephani's book.

In deriving the equations of motion for a force-free particle, we have the Lagrangian:

[tex]L = \frac{m}{2} g_{\alpha \beta} \dot{x}^\alpha \dot{x}^\beta[/tex]

To construct the equations of motion we need

[tex]\frac{\partial L}{\partial \dot{x}^\nu} = m g_{\alpha \nu} \dot{x}^\alpha[/tex]

and

[tex]\frac{\partial L}{\partial x^\nu} = L_{,\nu} = \frac{m}{2} g_{\alpha \beta, \nu} \dot{x}^\alpha \dot{x}^\beta[/tex]

Then from the Lagrange equations we get

[tex]g_{\alpha \nu }\ddot{x}^\alpha + g_{\alpha \nu, \beta} \dot{x}^\alpha \dot{x}^\beta - \frac{1}{2}g_{\alpha \beta, \nu}\dot{x}^\alpha \dot{x}^\beta =0[/tex]

I don't understand where the second term in the last equation comes from.

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

Join Physics Forums Today!

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

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

# Question about tensor derivative

Loading...

Similar Threads - Question tensor derivative | Date |
---|---|

A Two questions on the Stress-Energy Tensor | Jun 8, 2017 |

I A question about tensors | Oct 18, 2016 |

I Schnutz Special Relativity Tensors Question | Apr 17, 2016 |

Question about the metric tensor | Nov 9, 2015 |

Questions on tensors in GR and the Newtonian limit | Aug 27, 2015 |

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