What's dt in finding normal vector for curvature

[hivesaeed4]

A formula for finding the normal vector for curvature is:
N=(dT/ds)/(||dT/ds||)

Where
dT=change in tangent vector
ds=change in distance travelled

Another fromula was:

N=(dT/dt)/(||dT/dt||)


What's dt ?
Is it the same as ds? I don't think so cause the course notes said that calculations can be done more easily using the second formula.

 

[jppike]

t is a parameter that you would parametrize your curve with, usually thought of as time. However, there is a natural parameter, s, which in some sense measures the 'distance travelled' as you said. For more on the difference between an arbitrary parameter t and the natural parameter s, refer to this short section on Wikipedia:

http://en.wikipedia.org/wiki/Differential_geometry_of_curves#Length_and_natural_parametrization