Study Section 1.5 and solve the following exercises.
Section 1.5: 2, 3, 6, 8, 9, 10, 11, 12, 14. Remark: In Exercise 14, a reflection, claimed possibly needed in part (2), is in fact not necessary at all. Explain why, if you can. It is a flaw in the textbook.
"Why is the Frenet equations matrix skew?" The following problem explains why.
Problem X. Let [A,B,C] be an orthonormal moving frame, that is, a collection of three vectors A(t), B(t), C(t) in space, changing smoothly with time, such that at any moment t, each vector is unit and they are all orthogonal to each other. Show that the 3x3 matrix M describing the equations of motion:
[A',B',C'] = M [A,B,C],
where the brackets denote putting things in a column, is skew, that is,
M^T = - M.