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?

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# Differential of normal vector

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