Variational principles for the linear and adiabatic oscillations of a spherical star, and related definitions of canonical energy density and of canonical energy flux

Abstract

Abstract It is examined how the variational principle of Chandrasekhar and Lebovitz for adiabatic non-radial oscillations of a spherical star. and the variational principle for wave motions in a horizontal atmospheric layer given by Tolstoy stem for Hamilton's principle. The known variational functionals are recovered from the Lagrangian that is defined as the difference between the change in kinetic energy and the sum of the changes in the internal and gravitational potential energies. Certain terms of the Lagrangian vanish because of the boundary conditions of the star's equilibrium. The implications for the canonical energy densities and the canonical energy fluxes that are derived from the various Lagrangians are considered.