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GATE 2022 PH – Question 55

Classical Mechanics · canonical transformations: Poisson bracket. Special theory of relativity: Lorentz transformations, relativistic kinematics, mass-energy equivalence. · 2 marks · Multiple select

In action-angle variables, $H=4I_1I_2$, $0\le\theta_1,\theta_2<2\pi$, and $I_1/I_2=1/2$. Which plotted trajectories are possible?

Action-angle trajectories, including the continued option D.
  1. Option A in the figure
  2. Option B in the figure
  3. Option C in the figure
  4. Option D in the figure

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Show answer and explanation

Correct answer: (B) Option B in the figure; (C) Option C in the figure

Explanation

$\dot\theta_1=4I_2$ and $\dot\theta_2=4I_1$, so every unwrapped trajectory has slope 1/2 and winds twice in theta1 per theta2 cycle. B and C have the required slope and torus matching.