Calculus of variations
Example
2 π
ZT
0
x(t)
r
1 +
x
2
dt!min
x( 0 )=a,x(T)=b
The kernel is
F
t,x,x
=x
r
1 +
x
2
The EulerñLagrange is
r
1 +
x
2
= d
dt
r xx
1 +
x
2 π
ZT
0
x(t)
r
1 +
x
dt!min
x( 0 )=a,x(T)=b
The kernel is
F
t,x,x
=x
r
1 +
x
The EulerñLagrange is
r
1 +
x
= d
dt
r xx
1 +
x