- #1

S1000

- 1

- 0

- Homework Statement
- Find the Hamiltonian of a Point particle on a frictionless plane with a given potential (kr^2)/2

- Relevant Equations
- L = T - V

dot rep time derivative

L = (m/2) * ( rdot^2 + r ^2 θdot^2) - V (r,θ)

Lagrange eq

d/dt (∂L/∂xdot) = ∂L/∂x

H = Σ pi qdoti - L

a)

b)

c)

c) continued - and d) at the bottom of the page

d)

I can sub in p_r into the Hamiltonian in e) however, I cannot use the p_theta 'dot' expression.

and then also

for f) how to show the energy is equal to kr_0.