Question

Consider the Lagrangian \( L = m\dot{x}\dot{y} - mw_0^2 zxy \). If \( p_x \) and \( p_y \) denote the generalized momenta conjugate to \( x \) and \( y \), respectively, then the canonical equations of motion are _______.

• A. \(\dot{x} = \frac{P_x}{m} \), \(\dot{P_x} = -mw_0^2 x \), \(\dot{y} = \frac{P_y}{m} \), \(\dot{P_y} = -mw_0^2 y \)
• B. \(\dot{x} = \frac{P_x}{m} \), \(\dot{P_x} = mw_0^2 x \), \(\dot{y} = \frac{P_y}{m} \), \(\dot{P_y} = mw_0^2 y \)
• C. \(\dot{x} = \frac{P_y}{m} \), \(\dot{P_x} = -mw_0^2 y \), \(\dot{y} = \frac{P_x}{m} \), \(\dot{P_y} = -mw_0^2 x \)
• D. \(\dot{x} = \frac{P_y}{m} \), \(\dot{P_x} = mw_0^2 y \), \(\dot{y} = \frac{P_x}{m} \), \(\dot{P_y} = mw_0^2 x \)

Answer 1

The Correct Option is C

The correct option is (C) :\(\dot{x} = \frac{P_y}{m} \), \(\dot{P_x} = -mw_0^2 y \), \(\dot{y} = \frac{P_x}{m} \), \(\dot{P_y} = -mw_0^2 x \)