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

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elica85Best ResponseYou've already chosen the best response.1
curvature is the rate where the unit vector T turns per unit of length. it is calculated \[k=dT/ds\]
 2 years ago

elica85Best ResponseYou've already chosen the best response.1
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\[r'(t)/r'(t)\]
 2 years ago

elica85Best ResponseYou've already chosen the best response.1
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, \[s(t)= \int\limits_{t _{0}}^{t} (dx/dt)^{2}+(dy/dt)^{2}+(dz/dt)^{2} dt\]
 2 years ago

elica85Best ResponseYou've already chosen the best response.1
now, k can be re written as \[k=(dT/dt)(dt/ds)\]
 2 years ago

elica85Best ResponseYou've already chosen the best response.1
the purpose of finding an arc length can be thought of as wanting to know how sharp a curve is turning
 2 years ago

elica85Best ResponseYou've already chosen the best response.1
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
 2 years ago

elica85Best ResponseYou've already chosen the best response.1
calc III just had the finals on monday
 2 years ago
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