Abstract
Basic concepts, as the Lagrangian displacement of a mass element and the Lagrangian and Eulerian perturbations of a physical quantity, are presented in terms of both orthonormal Cartesian coordinates and generalised coordinates. Useful relations are established for the perturbations of partial derivatives of physical quantities with respect to time or to a spatial coordinate. An expression is also established for the Eulerian perturbation of a velocity component of a mass element in terms of its Lagrangian displacement. The last part of the chapter is devoted to the derivation of expressions for the perturbations of physical quantities which play an important role in stellar oscillations: the mass density, the gravitational potential, the pressure, and the temperature.
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References
S. Chandrasekhar (1969) Ellipsoidal Figures of Equilibrium. Yale University Press, New Haven
J.P. Cox (1980) Theory of Stellar Pulsation. The University Press, Princeton
F.A. Dahlen, J. Tromp (1998) Theoretical Global Seismology. The University Press, Princeton
J.L. Friedman, B.F. Schutz (1978) Lagrangian perturbation theory of nonrelativistic fluids. Astrophys. J. 221, 937–957
H. Goldstein (1957) Classical Mechanics. Addison-Wesley, Reading,
J.B. Hartle (2003) Gravity: An Introduction to Einstein’s General Relativity. Addison Wesley, San Francisco
S. Kato, W. Unno (1967) Pulsational instability of stars in quasi-equilibrium. Publ. Astron. Soc. Jpn. 19, 1–19
O.D. Kellogg (1929) Foundations of Potential Theory. Springer, Berlin
G.A. Korn, T.M. Korn (1968) Mathematical Handbook – for Scientists and Engineers. McGraw-Hill, New York
C.W. Misner (1969) Astrophysics and General Relativity, ed. by M. Chrétien, S. Deser, J. Goldstein. Gravitational collapse. Brandeis University, Summer Institute in Theoretical Physics, 1968, vol. 1. Gordon and Breach, New York, pp. 113–215.
C.W. Misner, K.S. Thorne, J.A. Wheeler (1973) Gravitation. Freeman, San Francisco
P.M. Morse, H. Feshbach (1953) Methods of Theoretical Physics. McGraw-Hill, New York
P.H. Roberts (1967) An Introduction to Magnetohydrodynamics. Longmans, London
J.-L. Tassoul (1978) Theory of Rotating Stars. The University Press, Princeton
A.H. Taub (1969) Stability of general relativistic gaseous masses and variational principles. Commun. Math. Phys. 15, 235–254
T. Van Hoolst (1992) Nonlinear, Nonradial Oscillations of Stars. Doctoral Dissertation, Katholieke Universiteit Leuven
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Smeyers, P. (2010). Basic Concepts. In: Linear Isentropic Oscillations of Stars. Astrophysics and Space Science Library, vol 371. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13030-4_2
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DOI: https://doi.org/10.1007/978-3-642-13030-4_2
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