1. …

2. However, there are more general symmetries that no coordinate system can fully express. For example, motion in a central potential is spherically symmetric … , but the expression of the Lagrangian for the system in spherical coordinates exhibits symmetry around only one axis.

3. …

4. A continuous symmetry is a parametric family of symmetries. Noether proved that for any continuous symmetry there is a conserved quantity.

— Structure and Interpretation of Classical Mechanics

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2023.10.23 Monday ACHK