The Lagrangian of a system is given by
L = \(\frac{1}{2}\) ml2[\(\dot \theta^2\) + sin2θ\(\dot \varphi^2\)] − mgl cos θ, where m, l and g are constants.
Which of the following is conserved?
1
\(\dot \varphi \sin^2 \theta\)
2
\(\dot \varphi \sin \theta\)
3
\(\frac{\dot{\varphi}}{\sin \theta}\)
4
\(\frac{\dot{\varphi}}{\sin ^{2} \theta}\)
5
Question Not Attempted