i need help on this please ! Suppose that the Lagrangian of an N-particle system

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i need help on this please !

Suppose that the Lagrangian of an N-particle system is unchanged by rotations about a certain symmetry axis. Taking this axis to be the z-axis, and using cylindrical coordinates, this symmetry is mathematically expressed as an invariance of the Lagrangian under rotating all particles (r alpha, Phi alpha, z alpha ) to (r alpha, Phi alpha + belongs, z alpha) alpha = 1 N. Show that this implies Use the Euler-Lagrange equations to then show that the total angular momentum Lz is a constant of motion.

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For as more formal proof of Noether

For as more formal proof of Noether

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