Hamiltonian canonical equations of motion for a conservation system are
A. $$\frac{{ - d{q_i}}}{{dt}} = \frac{{\partial H}}{{\partial {P_i}}}{\text{ and }}\frac{{ - d{P_i}}}{{dt}} = \frac{{\partial H}}{{\partial {q_i}}}$$
B. $$\frac{{d{q_i}}}{{dt}} = \frac{{\partial H}}{{\partial {P_i}}}{\text{ and }}\frac{{d{P_i}}}{{dt}} = \frac{{\partial H}}{{\partial {q_i}}}$$
C. $$\frac{{ - d{q_i}}}{{dt}} = \frac{{\partial H}}{{\partial {P_i}}}{\text{ and }}\frac{{d{P_i}}}{{dt}} = \frac{{\partial H}}{{\partial {q_i}}}$$
D. $$\frac{{d{q_i}}}{{dt}} = \frac{{\partial H}}{{\partial {P_i}}}{\text{ and }}\frac{{ - d{P_i}}}{{dt}} = \frac{{\partial H}}{{\partial {q_i}}}$$
Answer: Option D
This Question Belongs to Engineering Physics >> Classical Mechanics
A. increases till mass falls into hole
B. decreases till mass falls into hole
C. remains constant
D. becomes zero at radius r1, where 0 < r1 < r0
A. $$\frac{c}{3}$$
B. $$\frac{{\sqrt 2 }}{3}c$$
C. $$\frac{c}{2}$$
D. $$\frac{{\sqrt 3 }}{2}c$$
The Hamiltonian corresponding to the Lagrangian $$L = a{{\dot x}^2} + b{{\dot y}^2} - kxy$$ is
A. $$\frac{{{p_x}^2}}{{2a}} + \frac{{{p_y}^2}}{{2b}} + kxy$$
B. $$\frac{{{p_x}^2}}{{4a}} + \frac{{{p_y}^2}}{{4b}} - kxy$$
C. $$\frac{{{p_x}^2}}{{4a}} + \frac{{{p_y}^2}}{{4b}} + kxy$$
D. $$\frac{{{p_x}^2 + {p_y}^2}}{{4ab}} + kxy$$
A. circular
B. elliptical
C. parabolic
D. hyperbolic
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