The Hamiltonian of a two particle system is H = p1p2 + q1q2, where q1 and q2 are generalized coordinates and p1 and p2 are the respective canonical momenta. The Lagrangian of this system is
1
\(\dot{q}_1 \dot{q}_2+q_1 q_2\)
2
\(-\dot{q}_1 \dot{q}_2+q_1 q_2\)
3
\(-\dot{q}_1 \dot{q}_2-q_1 q_2\)
4
\(\dot{q}_1 \dot{q}_2-q_1 q_2\)