Question

The Hamiltonian’s equation of motion is

• A. $\dot{q}_j = \frac{\partial H}{\partial p_j}, \; \dot{p}_j = -\frac{\partial H}{\partial q_j}$
• B. $\dot{q}_j = \frac{\partial H}{\partial q_j}, \; \dot{p}_j = -\frac{\partial H}{\partial p_j}$
• C. $\dot{p}_j = \frac{\partial H}{\partial q_j}, \; \dot{q}_j = -\frac{\partial H}{\partial p_j}$
• D. $\dot{p}_j = -\frac{\partial H}{\partial p_j}, \; \dot{q}_j = \frac{\partial H}{\partial q_j}$

Hint:

Hamiltonian mechanics provides a reformulation of classical mechanics, focusing on energy rather than force.

Answer 1

The Correct Option is A

Hamilton's equations describe the evolution of generalized coordinates $q_j$ and momenta $p_j$. They are fundamental in classical mechanics for systems in phase space:
\[\dot{q}_j = \frac{\partial H}{\partial p_j}, \quad \dot{p}_j = -\frac{\partial H}{\partial q_j}\]