Register to reply

Probelm in calculating a First Variation

by muzialis
Tags: probelm, variation
Share this thread:
May1-12, 10:23 AM
P: 152

I am reading a paper on evolution problems of the type

u(0) = 0
u' (t) = v (t)
v(t) = argmin {G (t, u(t), v(t)}

The authour claims that the Euler Lagrange equation related to the last equation is

dG / dv = 0 (1)

I can not understand this.

The Euler Equation formally can be written as

dG / du - d (dG/dv) / dx (2)

and this equation will be satisifed by u.

But as the authour says, v satisfies
dG / dv = 0 (3)

u is the primitive of u, hence it should satisfy
d (dG/dv) / dx (4)

and this is different from (2)!

Any help please? I am confused. I attach the paper for completeness, equation (10) in the paper's introduction is the problem, which is self-contained between equations (4) and (10), quick to read for somebody with a clue...

Thank you!
Attached Files
File Type: pdf Larsen Fracture Paths.pdf (557.1 KB, 6 views)
Phys.Org News Partner Science news on
'Office life' of bacteria may be their weak spot
Lunar explorers will walk at higher speeds than thought
Philips introduces BlueTouch, PulseRelief control for pain relief

Register to reply

Related Discussions
Proportion of total variation is accounted for by explained variation Set Theory, Logic, Probability, Statistics 3
Variation of masses in lead-acid battery due to H2SO4 mass variation Biology, Chemistry & Other Homework 5
Equilibrium Probelm Introductory Physics Homework 3
Help with a probelm Introductory Physics Homework 12
A Probelm To far Introductory Physics Homework 2