calculus (advanced)

vector-valued functions

differentiating a vector-valued function by derivating of each of the components

(vector-valued function derivatives) sum and difference property

(vector-valued function derivatives) scalar product property

(vector-valued function derivatives) dot product property

(vector-valued function derivatives) cross product property

(vector-valued function derivatives) chain product property

r(t) ⋅ r(t) = constant ⇒ r(t) ⋅ r'(t) = 0

arc length function and it's derivative

curvature formulas

radius of curvature