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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.
The book presents a unified and well-developed approach to the dynamics of angular motions of rigid bodies subjected to perturbation torques of different physical nature. It contains both the basic foundations of the rigid body dynamics and of the asymptotic method of averaging. The rigorous approach based on the averaging procedure is applicable to bodies with arbitrary ellipsoids of inertia. Action of various perturbation torques, both external (gravitational, aerodynamical, solar pressure) and internal (due to viscous fluid in tanks, elastic and visco-elastic properties of a body) is considered in detail. The book can be used by researchers, engineers and students working in attitude dynamics of spacecraft.
Newtonian mechanics : dynamics of a point mass (1001-1108) - Dynamics of a system of point masses (1109-1144) - Dynamics of rigid bodies (1145-1223) - Dynamics of deformable bodies (1224-1272) - Analytical mechanics : Lagrange's equations (2001-2027) - Small oscillations (2028-2067) - Hamilton's canonical equations (2068-2084) - Special relativity (3001-3054).
The Solar System is a complex and fascinating dynamical system. This is the first textbook to describe comprehensively the dynamical features of the Solar System and to provide students with all the mathematical tools and physical models they need to understand how it works. It is a benchmark publication in the field of planetary dynamics and destined to become a classic. Clearly written and well illustrated, Solar System Dynamics shows how a basic knowledge of the two- and three-body problems and perturbation theory can be combined to understand features as diverse as the tidal heating of Jupiter's moon Io, the origin of the Kirkwood gaps in the asteroid belt, and the radial structure of Saturn's rings. Problems at the end of each chapter and a free Internet Mathematica® software package are provided. Solar System Dynamics provides an authoritative textbook for courses on planetary dynamics and celestial mechanics. It also equips students with the mathematical tools to tackle broader courses on dynamics, dynamical systems, applications of chaos theory and non-linear dynamics.
Each chapter has three types of learning aides for students: open-ended questions, multiple-choice questions, and quantitative problems. There is an average of about 50 per chapter. There are also a number of worked examples in the chapters, averaging over 5 per chapter, and almost 600 photos and line drawings.
Satellites are used increasingly in telecommunications, scientific research, surveillance, and meteorology, and these satellites rely heavily on the effectiveness of complex onboard control systems. This 1997 book explains the basic theory of spacecraft dynamics and control and the practical aspects of controlling a satellite. The emphasis throughout is on analyzing and solving real-world engineering problems. For example, the author discusses orbital and rotational dynamics of spacecraft under a variety of environmental conditions, along with the realistic constraints imposed by available hardware. Among the topics covered are orbital dynamics, attitude dynamics, gravity gradient stabilization, single and dual spin stabilization, attitude maneuvers, attitude stabilization, and structural dynamics and liquid sloshing.