T (tangent), B (binormal), N (normal) are an orthogonal triad of unit vectors of a curve in R3.
- dT/ds = kN
- dN/ds = -kT + tB
- dB/ds = -tN
Find vector w so that these equations may be written in the form:
dv/ds = w x v, where v = T + N + B
The Attempt at a Solution
I tried splitting v (T + N + B) into its components, as well as w, and putting them into a matrix to find the determinant (for the cross product).
The matrix consists of <i, j, k>, w = <w1, w2, w3>, and v = <(T1 + N1 + B1), (T2 + N2 + B2), (T3 + N3 + B3)>.
However, taking the determinant/cross product gives mismatching components (ie. j and k components supposedly add up to an i component). I'm not too sure where to go from here :(
Note: This is for a Multivariate Calculus course!