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

I am having some frustration understanding one derivation of the Euler Lagrange Equation. I think it most efficient if I provide a link to the derivation I am following (in wikipedia) and then highlight the portion that is giving me trouble.

The link is here

If you scroll down to "Derivation of one-dimensional Euler–Lagrange equation".

I am confused on the following two lines under "It follows from the total derivative that..."

[tex] \frac{dF_\epsilon}{d\epsilon} = \frac{\partial F}{\partial \epsilon} + \frac{dx}{d\epsilon}\frac{\partial F}{\partial x} + \frac{dg_\epsilon}{d\epsilon}\frac{\partial F}{\partial g_\epsilon} +\frac{dg'_\epsilon}{d\epsilon}\frac{\partial F}{\partial g'_\epsilon}[/tex]

[tex] \frac{dF_\epsilon}{d\epsilon} = \frac{dg_\epsilon}{d\epsilon}\frac{\partial F}{\partial g_\epsilon} +\frac{dg'_\epsilon}{d\epsilon}\frac{\partial F}{\partial g'_\epsilon}[/tex]

It is not clear to me why the first two terms are zero. I assume that the second term is zero because [itex]x[/itex] is constant with respect to [itex]\epsilon[/itex]. But, I do not know why the partial of [itex]F_e[/itex] is zero.

Any help would be appreciated, thank you!

Will

**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!

# Help with Derivation of Euler Lagrange Equation

Loading...

Similar Threads - Help Derivation Euler | Date |
---|---|

I Please help with nth derivative question | Nov 2, 2017 |

I Re-derive the surface area of a sphere | Aug 28, 2016 |

I Need help with derivative notation | Aug 7, 2016 |

B I need help with a related rates question | Jul 24, 2016 |

Help with derivation of euler-lagrange equations | Nov 21, 2009 |

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