- #1

mma

- 245

- 1

In Newtonian mechanics, conservation laws of momentum and angular momentum for an isolated system follow from Newton's laws plus the assumption that all forces are central. This picture tells nothing about symmetries.

In contrast, in Hamiltonian mechanics, conservation laws are tightly connected to symmetries. A symmetry is a one-parameter Lie group with a symplectic group action on phase space that preserves Hamiltonian (a Hamiltonian-preserving symplectic flow), and the infinitesimal generator of this flow is a conserved quantity.

However, the standard symplectic Hamiltonian description is less general than Newton's law because dissipative forces aren't incuded. So, it seems that Newton's conservation laws are more general then the Hamiltonian ones. Is there any attempt for achieving the same generality by symmetry considerations, as Newtonian description have?

In contrast, in Hamiltonian mechanics, conservation laws are tightly connected to symmetries. A symmetry is a one-parameter Lie group with a symplectic group action on phase space that preserves Hamiltonian (a Hamiltonian-preserving symplectic flow), and the infinitesimal generator of this flow is a conserved quantity.

However, the standard symplectic Hamiltonian description is less general than Newton's law because dissipative forces aren't incuded. So, it seems that Newton's conservation laws are more general then the Hamiltonian ones. Is there any attempt for achieving the same generality by symmetry considerations, as Newtonian description have?

Last edited: