[QUE/CM-04015]

For relativistic particle of mass \(m\) in  three dimensions the  Hamiltonian is given by  \( H= \sqrt{\vec{p}^{\,2} c^2 +m^2c^4}\).

1. Obtain the Hamiltonian equations of motion.
2. Derive the Lagrangian and write Euler Lagrange equations of motion.