Are there any facts about the derivative of the normalised normal vector n to a surface embedded in n-dimensional Euclid space? Is it true, for instance, that(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\frac{\partial n_j}{\partial x^i} = \frac{\partial n_i}{\partial x^j}[/tex]

The context is as follows. The surface is defined implicitly by a constraint function; there's a Hamiltonian in reduntant coordinates and the canonical Hamiltonian equations of motion for (q,p) ensuring that trajectories lie in the constraint surface. I need to find acceleration [itex]\ddot{q}[/itex]; there the time derivative of n appears. By the way, how could I reformulate this task in the language of differential geometry?

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

Dismiss Notice

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!

# Differential of normal vector

Loading...

Similar Threads for Differential normal vector | Date |
---|---|

A How to calculate the second fundamental form of a submanifold? | Monday at 9:54 AM |

I Diffeomorphism invariance and contracted Bianchi identity | Apr 13, 2018 |

A Smoothness of multivariable function | Apr 10, 2018 |

A Smooth extension on manifolds | Apr 5, 2018 |

A Degree of Gauss normal map | Nov 30, 2016 |

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