Calculus of variations
Zb
a
F
t,x,x
dt! maxmin
x(a)=xa,x(b)=xb
Letybe an arbitrary function, called variation, withy(a)=y(b)= 0 .Let
ψ(λ)$
Zb
a
F
t,x(t)+λy(t),x(t)+λy(t)
dt
Ifxis an optimal function then by Fermatís principleψ^0 ( 0 )= 0.
Zb
a
t,x,x
dt! maxmin
x(a)=xa,x(b)=xb
Letybe an arbitrary function, called variation, withy(a)=y(b)= 0 .Let
ψ(λ)$
Zb
a
t,x(t)+λy(t),x(t)+λy(t)
dt
Ifxis an optimal function then by Fermatís principleψ^0 ( 0 )= 0.