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Arc length of a vector function <x(t), y(t), z(t)>

Unit tangent vector T of r(t)

Curvature given arc length parametrization and T

How to relate arc length to r(t)
ds/dt = r'(t)

Curvature given T and r(t)

Curvature given only r(t)

Curvature of a plane curve given y = f(x)


Find N given B and T
N = B x T

How to find the normal plane
Use T(t) as the normal and r(t) for a given point t on the curve

How to find the osculating plane
Use B(t) as the normal and r(t) for a given point t

v(t) given r(t)
v(t) = r'(t)

a(t) given r(t)
a(t) = r''(t) = v'(t)

v given T
V = vT = vT

Tangential component of acceleration given r(t) and T
r'(t) T = T

normal component of acceleration given r(t)

