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

Answer: (C)

$\dot{x} = \frac{P_y}{m}$, $\dot{P_x} = -mw_0^2 y$, $\dot{y} = \frac{P_x}{m}$, $\dot{P_y} = -mw_0^2 x$

Answer 2

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