Proving Curvature Formulas: V X A / l V3l and a(t) * N(t) / l V(t) I2

  • Thread starter Thread starter Baumer8993
  • Start date Start date
  • Tags Tags
    Curvature Proofs
Click For Summary
SUMMARY

The discussion focuses on proving two curvature formulas: (V X A) / |V|^3 and a(t) * N(t) / |V(t)|^2. The user expresses confusion regarding the application of these formulas, particularly in transforming acceleration into the required vector cross product form and incorporating the cube of the speed. The need for visual aids, such as YouTube videos, is highlighted to facilitate understanding of these concepts.

PREREQUISITES
  • Understanding of vector calculus and cross products
  • Familiarity with curvature concepts in differential geometry
  • Knowledge of the Frenet-Serret formulas, specifically T(t), N(t), and their roles in motion
  • Basic proficiency in physics, particularly kinematics and acceleration
NEXT STEPS
  • Watch YouTube tutorials on vector calculus and curvature formulas
  • Study the derivation of the Frenet-Serret formulas in detail
  • Practice problems involving vector cross products and their applications in curvature
  • Explore resources on the geometric interpretation of acceleration and curvature
USEFUL FOR

Students studying physics or mathematics, particularly those focusing on vector calculus and curvature in motion, as well as educators seeking to clarify these concepts for their students.

Baumer8993
Messages
45
Reaction score
0

Homework Statement


I have to prove two of the curvature formulas. The first one is (V X A) / l V3l

The other one is a(t) * N(t) / l V(t) I2


Homework Equations



I have a hint from my professor, but it is all confusing. I need a youtube video or something to get started on these.

The Attempt at a Solution



I used the a(t) = at *T + an*N to get the first part, but now I am stuck on the making it into the form of V X A. The I have no idea how I would get it over the cube of the speed.
 
Physics news on Phys.org
These don't seem to be equations. There are no equals signs. Can you edit and tell us what you mean?
 

Similar threads

  • · Replies 1 ·
Replies
1
Views
3K
  • · Replies 24 ·
Replies
24
Views
4K
  • · Replies 1 ·
Replies
1
Views
1K
Replies
15
Views
3K
Replies
5
Views
2K
Replies
8
Views
2K
  • · Replies 7 ·
Replies
7
Views
1K
Replies
6
Views
3K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K