Conservation of Angular Momentum Using the Hamiltonianby physics2018 Tags: angular momentum, hamiltonian, invariant, lagrangian, particle 

#1
Oct1509, 09:00 AM

P: 1

1. The problem statement, all variables and given/known data
The Hamiltonian for a particle mass m, moving in a central force field is given as: H = 1/(2m) * p^2  V(r). Take the Hamiltonian to be invariant, such that it can be shown that L = r x p the angular momentum vector is a conserved quantity: dL/dt = {L,H} = 0. 2. Relevant equations q_idot = dH/dp_i and p_idot =  dH/dq_i 3. The attempt at a solution I do not understand how to go about solving the following problem ( I think I understand what the Hamiltonian is, but I do not understand how to from it to what needs to be proven) To solve the problem I believe I need to get from Hamiltonian's equations to Lagrange's p_i = dL/dx_idot and then from there use pdot * dr + p * drdot = 0 where dr is defined as the distance between two vectors r and r+dr. 


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