Consider the Lagrangian \(L=a(\frac{dx}{dt})^2+b(\frac{dy}{dt})^2+cxy,\) where a, b and c are constants. If \(p_x\quad and \quad p_y\) are the momenta conjugate to the coordinates x and y respectively, then the Hamiltonian is:
1
\(\frac{p_x^2}{4a}+\frac{p_y^2}{4b}-cxy\)
2
\(\frac{p_x^2}{2a}+\frac{p_y^2}{2b}-cxy\)
3
\(\frac{p_x^2}{2a}+\frac{p_y^2}{2b}+cxy\)
4
\(\frac{p_x^2}{a}+\frac{p_y^2}{b}+cxy\)
5
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