In most books on classical mechanics, Noether's Theorem is only formulated in conservative systems with an action principle. Therefore I was wondering if it is possible to also do that in non-conservative systems? It would be pretty cool if you could at least get the conservation of momentum (which is valid also in non-conservative systems if there are no external forces because of Newton 3) from translation symmetry and conservation of angular momentum (which is also valid in non-conservative systems as long as there are only central forces) as a consequence of rotation symmetry in non-conservative systems. If that is not the case, is there any way to extend Hamilton's principle or the generelization of it ($\int (\delta T + \delta W) dt = 0$, see for example Sommerfeld) so that it also covers Newton 3 (also maybe that's a topic worthy of its own question)?



Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.