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23 Nov 2019
Consider the Lagrangian L = (m/2)(x'2 +y'2 + z'2). Derive its Hamiltonian H =Σpkq'k - L
a) in cylindrical coordinates and
b) in spherical coordinates.
In cylindrical coordinates, the Langrangian is(m/2)(r'2 + r2θ'2+z'2).
In spherical coordinates, the Lagrangian is (m/2)(r'2+ r2θ'2 +r2Ï'2sin2θ).
Consider the Lagrangian L = (m/2)(x'2 +y'2 + z'2). Derive its Hamiltonian H =Σpkq'k - L
a) in cylindrical coordinates and
b) in spherical coordinates.
In cylindrical coordinates, the Langrangian is(m/2)(r'2 + r2θ'2+z'2).
In spherical coordinates, the Lagrangian is (m/2)(r'2+ r2θ'2 +r2Ï'2sin2θ).