/sci/ - Science & Math

Hello, /sci/. I have a question to ask:
If i have field data of accelerations on a Frenet-Serret orthonormal basis, what can i do to figure out how this basis changes with respect to a similar orthonormal basis,{i, j, k}, that does move with the particle but that does not rotate as it does, with the purpose of eliminating the measured acceleration of -9.8 m/s2 in the k direction from my {T, N, B} acceleration data?
I believe my data is inflated because of the presence of this -9.8 m/s^2k:
when i numerically integrate to find velocities and positions, i find unrealistic numbers.

>>8625103

> elder god of the 32nd dimension tier
> geometry

My man! Lookin' good!

How tf am I supposed to visualize/conceptualize connection forms?

Things I understand:

>a 1-form, df, is the outside derivative of a real valued function, f: R^n --> R,
>and a k-form is just the outside derivative of a (k-1)-form

>if f: R^3 --> R, then df: R^3 x R^3 --> R
>So, df takes a point and a vector and shows how f varies at the point in the vector's direction

>If you take the covariant derivative of one frame field to another, you get a matrix of 1-forms, called connection forms

So what is special about the (1,2) and (1,3) entries, but not the (2,3) entry? Like, how does this relate to the shape operator?