## nadia_g Group Title can some one give me the concept of arc and curvature( related to calculus 3) 2 years ago 2 years ago

1. elica85

curvature is the rate where the unit vector T turns per unit of length. it is calculated $k=|dT/ds|$

2. elica85

if you are given a position, you can find T by dividing the derivative of position over the absolute value of it. it can be looked at as velocity over speed$r'(t)/|r'(t)|$

3. elica85

ds refers to arc length parameter for a curve. if you're given a curve r(t)=x(t)i+y(t)j+z(t)k, $s(t)= \int\limits_{t _{0}}^{t} (dx/dt)^{2}+(dy/dt)^{2}+(dz/dt)^{2} dt$

4. elica85

now, k can be re written as $k=|(dT/dt)(dt/ds)|$

hmm.........ok thanx

elica?

7. elica85

the purpose of finding an arc length can be thought of as wanting to know how sharp a curve is turning

8. elica85

i just finished this class so my explanation might not be detailed enough since i need to understand more but i shared what i can