Central Force Problem

Energy Function
• Suppose L can be written as
L( q, q, t) = L ( q, t) + L ( q, q, t) + L ( q, q, t)
• True in most cases
of interest
• Derivatives satisfy
∂L
∂q
0
0
j
=
∑ q
j
0 1 2
j
∂L
∂q
1
j
=
L
1
1 st order in q
∑ q
j
j
∂L
∂q
2
j
2 nd order in q
= 2L
∂L
hqqt ( , , ) ≡ ∑ qj
− L= L −L
j ∂q
j
2 0
∂L
hqqt ( , , ) ≡ ∑ qj
− L
∂q
2
j
Euler’s
theorem
j