For Hamiltonian systems, symmetries and conservation laws are defined and related to each other by Noether's theorem. Symmetry means the invariance of the Hamiltonian for a transformation group, and the notion of momentum and angular momentum is also defined by the use of the Hamiltonian.
Cats are highly non-hamiltonian (and non-lagrangian) systems, yet in a free falling and rotation-free reference system, they also obey the law of conservation of momentum and angular momentum when they are in free fall. In this case, momentum and angular momentum aren't related to any Hamiltonian, Lagrangian or potential, they are simply the quantities which are used by Newton. Of course, the conservation of momentum and angular momentum can be derived from Newton's laws (if we suppose that all forces are central), but this derivation doesn't provide the relation between symmetries and conservation laws.
My question:
- How can symmetry be defined for a non-hamiltonian (and non-lagrangian) system (like a cat)?
- How can we relate symmetries to conservation laws in these systems?
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