Curvature Formulas

0.0(0)
studied byStudied by 0 people
learnLearn
examPractice Test
spaced repetitionSpaced Repetition
heart puzzleMatch
flashcardsFlashcards
Card Sorting

1/17

encourage image

There's no tags or description

Looks like no tags are added yet.

Study Analytics
Name
Mastery
Learn
Test
Matching
Spaced

No study sessions yet.

18 Terms

1
New cards

Curvature for arbitrary regular parametrizations

function in vector form

<p>function in vector form</p>
2
New cards

Curvature at a point on the graph y = f(x)

function in standard form

<p>function in standard form</p>
3
New cards

When is a parametrization r(t) regular?

r’(t) is not equal to 0

<p>r’(t) is not equal to 0</p>
4
New cards

When r(t) is a regular parametrization, what is T(t) (the unit tangent vector) defined as?

derivative of vector parametrization divided by the magnitude of the derivative of the vector parametrization

<p>derivative of vector parametrization divided by the magnitude of the derivative of the vector parametrization</p>
5
New cards

Curvature in terms of the s function

K = ||T’(s)||

<p>K = ||T’(s)||</p>
6
New cards

s (the arc length function) is equal to

integrate

<p>integrate</p>
7
New cards

How to find t in terms of s

isolate for t with the original function s(t)

<p>isolate for t with the original function s(t) </p>
8
New cards

N(t) (unit normal vector) =

T’(t)/||T’(t)||

<p>T’(t)/||T’(t)||</p>
9
New cards

Binormal Vector

B(t) =

B(t) = N(t) x T(t)

<p>B(t) = N(t) x T(t)</p>
10
New cards

How to find center of osculating circle?

r(t0) + 1/Kp * N

<p>r(t<sub>0</sub>) + 1/K<sub>p</sub> * N</p>
11
New cards

Equation of a plane

(a,b,c) * (x-x0, y-y0, z - z0)

<p>(a,b,c) * (x-x<sub>0</sub>, y-y<sub>0</sub>, z - z<sub>0</sub>)</p>
12
New cards

How to find equation of osculating plane

Dot product of Binomial vector + point on graph

13
New cards

T’(t)

T’(t) = k(t) * v(t) * N(t)

<p>T’(t) = k(t) <em>* </em>v(t) * N(t)</p>
14
New cards

aT =

(remember the 3 main formulas, mainly the first two)

3 main formulas

<p>3 main formulas</p>
15
New cards

aTT =

help

<p>help</p>
16
New cards

aN =

2 main formulas

in terms of curvature and sqrt version

<p>in terms of curvature and sqrt version</p>
17
New cards

aN =
cross product formula

Not in the textbook

<p>Not in the textbook </p>
18
New cards