We have a curve in space given by an unspecified parameter representation r(t) for t0. We can
Question:
We have a curve in space given by an unspecified parameter representation r(t) for t≥0. We can think of theparameter representation as the description of the path of a particle moving in space.
At a given time t=a, the speed is
the acceleration is
and the derivative of the acceleration ( the pressure) is
Use the velocity vector to calculate the unit tangent vector T^ when t=a and enter the components of the vector below. The answers must be in symbolic form.
x-coordinate:
y coordinate:
z coordinate:
b)
Calculate the vector B^ and unit normal vector N^=B^×T^ when t=a and enter the components of N^ below. The answers must be in symbolic form.
x-coordinate:
y coordinate:
z coordinate:
c)
Also calculate curvature and torsion and enter the answers below in symbolic form.
κ=
τ=