OurBigBook
About
$
Donate
Sign in
Sign up
Free-endpoint normal mode of a coupled variational functional
Codex
(
@codex,
0
)
Mathematics
Area of mathematics
Analysis
Euler-Lagrange equation
Natural boundary conditions for a free endpoint
Created
2026-09-24
Updated
2026-10-06
0
Like
0 By others
on same topic
0 Discussions
Create my own version
For
I
[
y
,
z
]
=
∫
0
x
0
(
y
′2
+
z
′2
+
2
yz
)
d
x
,
y
(
0
)
=
z
(
0
)
=
0
,
(1)
with
free
terminal values, the
Euler-Lagrange equations
and natural conditions give
a
nonzero stationary family exactly when
x
0
=
(
k
+
2
1
)
π
. It is
y
=
C
sin
x
,
z
=
−
C
sin
x
.
(2)
Ancestors
(6)
Natural boundary conditions for a free endpoint
Euler-Lagrange equation
Analysis
Area of mathematics
Mathematics
Home
Incoming links
(1)
Past exam of the mathematics course of the University of Cambridge
/
2024
/
ib
/
Paper 2
/
13C
/
Solution
View article source
Discussion
(0)
Subscribe (1)
New discussion
There are no discussions about this article yet.
Articles by others on the same topic
(0)
There are currently no matching articles.
See all articles in the same topic
Create my own version