2) How Much Does A Curve Curve? Flashcards
1
Q
Define curvature of a curve at a point
A
Curve must be unit speed parametrised
κ(s) at γ(s) is given
2
Q
Curvature of reg curve in r^n ?
A
3
Q
Regular curve
A
4
Q
A
5
Q
In 2d
A
6
Q
A
7
Q
A
8
Q
A
9
Q
γ(s) is a unit speed plane curve
A
10
Q
Describe
A
11
Q
A
12
Q
A
13
Q
A
14
Q
A
15
Q
A
16
Q
A
17
Q
A
18
Q
A
19
Q
A
20
Q
A
21
Q
A
For a unit speed curve in R^3
Unit tangent vector t
If curvature κ(s) is non zero
22
Q
A
23
Q
Right handed orthonormal basis of R^3
A
24
Q
A
25
Q
A
26
Q
Torsion is only defined if
A
Curvature is non zero
27
Q
Prove
A
28
Q
Frenet Serret equations
A
29
Q
Derive frenet serret equations
A
30
Q
Prove that a unit speed curve in R^3 with constant curvature and zero torsion is part of a circle
A
31
Q
Requirements for a rigid motion in R^3
A
