MediumCalculusca-129

Hamiltonian from Lagrangian

Problem

For L(q, qdot) = 0.5*m*qdot^2 + c*q*qdot - 0.5*k*q^2, the conjugate momentum is p = m*qdot + c*q.

Eliminating qdot = (p - c*q) / m gives H(q, p) = (p - c*q)^2 / (2*m) + 0.5*k*q^2. Given the parameters and (q, p), return H.

Hint

The Hamiltonian is the Legendre transform of the Lagrangian in the velocity.

case 1

in: [1,0,1,1,0]

expected: 0.5

case 2

in: [2,0,0,0,4]

expected: 4

case 3

in: [1,1,2,1,3]

expected: 3

case 4

in: [2,-1,4,2,1]

expected: 10.25

Starter codePython

def hamiltonian_from_lagrangian(m, c, k, q, p):
    # Your code here
    pass

4 test cases · run your code against them in the editor