2010/02/25 by S. A. Bludman, Bludman, Sidney, Dallas C. Kennedy +1
Earth and Planetary Sciences · Physics and Astronomy · #Astro and Planetary Science #Classical Physics (physics.class-ph) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Marine and environmental studies #Mathematical Physics (math-ph) #Solar and Stellar Astrophysics (astro-ph.SR) #Stellar, planetary, and galactic studies
paper · pdf · doi:10.48550/arxiv.1002.4670
openalex publication_date 2010/02/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Scaling symmetries of the Euler-Lagrange equations are generally not variational symmetries of the action and do not lead to conservation laws. Nevertheless, by an extension of Noether's theorem, scaling symmetries lead to useful \em nonconservation laws, which still reduce the Euler-Lagrange equations to first order in terms of scale invariants. We illustrate scaling symmetry dynamically and statically. Applied dynamically to systems of bodies interacting via central forces, the nonconservation law is Lagrange's identity, leading to generalized virial laws. Applied to self-gravitating spheres in hydrostatic equilibrium, the nonconservation law leads to well-known properties of polytropes describing degenerate stars and chemically homogeneous nondegenerate stellar cores.