How do i maximize the line integral?

Click For Summary
SUMMARY

The discussion centers on maximizing the line integral in a nonconservative vector field between two points, A and B. It highlights that without constraints on the coordinates or the length of the curve, the problem may be undefined. The conversation also introduces the concept of the Euler-Lagrange equation, indicating its relevance to solving such calculus of variations problems, particularly when considering paths that may circle against the flow of the vector field.

PREREQUISITES
  • Understanding of nonconservative vector fields
  • Familiarity with line integrals
  • Knowledge of calculus of variations
  • Proficiency in the Euler-Lagrange equation
NEXT STEPS
  • Study the properties of nonconservative vector fields
  • Explore the concept of line integrals in depth
  • Learn about the calculus of variations and its applications
  • Investigate the Euler-Lagrange equation and its derivations
USEFUL FOR

Mathematicians, physicists, and engineering students interested in advanced calculus, particularly those working with vector fields and optimization problems in physics.

okkvlt
Messages
53
Reaction score
0
suppose i have a nonconservative vector field.
and there is a path going from point A to point B.
How do i determine the path taken from A to B such that the line integral is maximized?
edit: actually after thinkin about it, this might be an undefined problem unless there is some constraint on the x,y,z coordinates.
 
Last edited:
Physics news on Phys.org
okkvlt said:
actually after thinkin about it, this might be an undefined problem unless there is some constraint on the x,y,z coordinates.

And on the length of the curve. Suppose a vector field circles the destination counterclockwise. What's to stop you from circling against the flow, round and round...
 
That is a "calculus of variations" problem. Do you know about the Euler-Lagrange equation?
 

Similar threads

Undergrad Equivalence of alternative definitions of conservative vector fields and line integrals in different metric spaces
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Help with a 3D Line Integral Problem (segmented line)
  • · Replies 14 ·
Replies
14
Views
2K
MHB How to prove this corollary in Line Integral using Riemann integral
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Is My Calculus of Variations Approach Correct?
  • · Replies 12 ·
Replies
12
Views
3K
Undergrad How to Calculate Surface Integral Using Stokes' Theorem?
  • · Replies 1 ·
Replies
1
Views
3K
Insights An Overview of Complex Differentiation and Integration
  • · Replies 1 ·
Replies
1
Views
4K
Graduate Maximization Problem: Double Int. w/ C not Dependent on Integrals
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Solving Line Integral Limits: Negative Result?
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad Green's theorem and Line Integrals
  • · Replies 1 ·
Replies
1
Views
2K
High School How do physicists know if limits exist, things are integrable, etc?
  • · Replies 12 ·
Replies
12
Views
3K