The Euler-Lagrange equations give a necessary condition for the action be extremal given some lagrangian which depends on some function to be varied over. The basic form assumes fixed endpoints for the function to be varied over, but we can extend to cases in which one or both endpoints are free to vary by introducing additional transversality conditions. I would like to know what the transversality condition(s) would be in the case that the values at the two boundaries are equal, but otherwise free to vary. The reason for this is that I want to consider functions which map the circle onto the real numbers, and use the calculus of variations approach to maximise an action based on a lagrangian of this function.(adsbygoogle = window.adsbygoogle || []).push({});

Thanks!

**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!

# Calculus of variations with circular boundary conditions

Loading...

Similar Threads - Calculus variations circular | Date |
---|---|

I Euler’s approach to variational calculus | Feb 18, 2018 |

A Maximization problem using Euler Lagrange | Feb 2, 2018 |

A Maximization Problem | Jan 31, 2018 |

A Derivation of Euler Lagrange, variations | Aug 26, 2017 |

I Calculus of variations | Aug 19, 2017 |

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