Studied by 2 peopleparameterize arc length
int a to b, abs value of r’ (u) du
curvature equation 1
|T’(t)| / |r’(t)|
curvature equation 2
|r’(t) x r’’(t)| / |r’(t)| ^ 3
special curvature equation
|f’’(x)| / (1 + f’(x)^2)^3/2
radius of circle
1/k
normal plane direction
r’(t)
osculating plane direction
r’(t) x r’’(t)
motion in space: normal acceleration
|r’(t) x r’’(t)| / |r’(t)|
motion in space: tangential acceleration
r’(t) dot r’’(t) / |r’(t)|
unit T(t)
r’(t) / |r’(t)|
unit N(t)
T’(t) / |T’(t)|
normal plane equation
Law of vectors
TNB
osculating plane equation
r’(t) x r’’(t) < x-x0, y-y0, z-z0?
Note
Flashcard