Question

Can someone explain to me what the derivative of a unit tangent vector IS????? I know how to find it but what does it represent?

Answer 1

it's the change of "velocity" if you treat the curve like path of the particle

Answer 2

so if it is the change of velocity is that acceleration?

Answer 3

I ask simply because I am in a section in my text book where they are asking me to take the derivative of the unit tangent vector. in my mind I am like "why what does that do?" then they want me to divide it by the directional vector it was derived from and I can't make sense of it.

Answer 4

are you in 2d or 3d?

Answer 5

3d

Answer 6

read into directional derivatives and gradients
no longer, in 3d, can we just have -,+ represent direction because there are infinite directions

directional derivatives are just that, the derivative in some direction
gradients are the direction of the steepest "slope".

also in 3d we would be talking about tangent planes because tangent vectors do not give much information.

Answer 7

Yeah my professor said we are not covering tangent planes because in a later section he will be discussing something else that will make it un-necessaty.

Answer 8

so are you looking at like vector equations for lines?
\[r=r_0+tv\]

Answer 9

I know that the derivative of a unit tangent vector divided by the derivative of the directional vector it was derived from give you the curvature of the graph. But I don't understand what just the derivative of the unit tangent vector by itself rep resents, or why you would divide the unit tangent vector by just the original directional vector, does not make sense. And no we are past that.