Suitable for upper-level undergraduates and graduate students, this text explores the most exact methods used in the theory of figures of equilibrium. It also examines problems concerning the figures of celestial bodies, including invariable or varying figures, zonal rotation, systems composed of fluid and rigid parts, and more. 1958 edition.

This volume pulls together more than forty years of research to provide graduate students and researchers in astrophysics, gravitational physics, and astronomy with the first self-contained treatment of the structure, stability, and oscillations of rotating neutron stars.

This book develops a general approach that can be systematically refined to investigate the statics and dynamics of deformable solid bodies. These methods are then employed to small bodies in the Solar System. With several space missions underway and more being planned, interest in our immediate neighbourhood is growing. In this spirit, this book investigates various phenomena encountered in planetary science, including disruptions during planetary fly-bys, equilibrium shapes and stability of small rubble bodies, and spin-driven shape changes. The flexible procedure proposed here will help readers gain valuable insights into the mechanics of solar system bodies, while at the same time complementing numerical investigations. The technique itself is built upon the virial method successfully employed by Chandrasekhar (1969) to study the equilibrium shapes of spinning fluid objects. However, here Chandrasekhar’s approach is modified in order to study more complex dynamical situations and include objects of different rheologies, e.g., granular aggregates, or “rubble piles”. The book is largely self-contained, though some basic familiarity with continuum mechanics will be beneficial.

Dynamics of Stellar Systems focuses on the theoretical problems in stellar dynamics. The book first offers information on stellar dynamics, including historical development, fundamentals of synthetic method, and value of stellar dynamics. The text discusses the fundamental concepts of stellar statistics. Properties of univariate distribution functions; multivariate distribution functions; and statistical properties of stars are explained. The text then describes the elementary theory of galactic rotation and irregular forces in stellar systems. The text also tackles statistical stellar dynamics of neglecting encounters. Considerations include Boltzmann equation in curvilinear coordinates; importance of using one-valued integrals of the motion; and fundamental differential equation of stellar dynamics. The book also underscores the regular orbit of stars and dynamics of centroids. The text describes the dynamics of spherical stellar and rotating stellar systems. The theory of polytropic spheres; basic equations for spherical systems; masses and rotation of galaxies; and boundaries of galaxies are discussed. The text is highly recommended for readers interested in stellar dynamics.

This scientific biography of the mathematician Joseph Liouville is divided into two parts. The first part is a chronological account of Liouville's career including a description of the institutions he worked in, his relations with his teachers, colleagues and students, and the historical context of his works. It portrays the French scientific community in a period when Germany and England had surpassed France as the leading nations in mathematics and physics. The second part of the book gives a detailed analysis of Liouville's major contributions to mathematics and mechanics. The gradual development of Liouville's ideas, as reflected in his publications and notebooks, are related to the works of his predecessors and his contemporaries as well as to later developments in the field. On the basis of Liouville's unpublished notes the book reconstructs Liouville's hitherto unknown theories of stability of rotating masses of fluid, potential theory, Galois theory and electrodynamics. It also incorporates valuable added information from Liouville's notes regarding his works on differentiation of arbitrary order, integration in finite terms, Sturm-Liouville theory, transcendental numbers, doubly periodic functions, geometry and mechanics.