Methods of Analytical Dynamics by Leonard Meirovitch: A Review
Methods of Analytical Dynamics is a book by Leonard Meirovitch that covers the fundamentals and applications of analytical dynamics, a branch of mechanics that deals with the motion of rigid and deformable bodies under the influence of forces. The book was first published in 1970 by McGraw-Hill and has been reprinted by Dover Publications in 2010.
The book aims to provide a balanced presentation that encompasses both formalism and structure in analytical dynamics, as well as solution methods. It employs an approach that is as natural as it is logical, using vector and tensor notation throughout. The book also covers topics that are usually not found in graduate courses in dynamics and nonlinear mechanics, such as transformation theory, the Hamilton-Jacobi equation, the theory and applications of the gyroscope, and problems in celestial mechanics and spacecraft dynamics.
Meirovitch Methods Of Analytical Dynamics Pdf Freel
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The book consists of 13 chapters and two appendices. The first chapter introduces the fundamentals of Newtonian and analytical mechanics, including the principle of virtual work, D'Alembert's principle, Lagrange's equations, and Hamilton's principle. The second chapter discusses motion relative to rotating reference frames, such as the Coriolis and centrifugal forces. The third chapter deals with rigid body dynamics, including Euler's equations, angular momentum, kinetic energy, and inertia dyadics. The fourth chapter explores the behavior of dynamical systems, such as equilibrium points, linearization, stability, bifurcations, and chaos. The fifth chapter presents the geometric theory of analytical dynamics, such as configuration space, phase space, constraints, holonomic systems, and nonholonomic systems. The sixth chapter studies the stability of multi-degree-of-freedom autonomous and nonautonomous systems, using Lyapunov's direct method and Floquet's theory. The seventh chapter introduces analytical solutions by perturbation techniques, such as regular and singular perturbations, averaging methods, and multiple scales methods. The eighth chapter develops transformation theory, such as canonical transformations, generating functions, Poisson brackets, and Liouville's theorem. The ninth chapter derives the Hamilton-Jacobi equation and its applications to integrable systems and action-angle variables. The tenth chapter explains the theory and applications of the gyroscope, such as precession, nutation, torque-free motion, Euler angles, and gyroscopic stabilization. The eleventh chapter addresses problems in celestial mechanics and spacecraft dynamics, such as Kepler's problem, two-body problem, three-body problem, restricted problem, Lagrange points, orbital elements, orbital maneuvers, attitude control, and attitude dynamics. The twelfth chapter reviews some special topics in analytical dynamics,
such as variational principles for nonconservative systems,
Hamilton-Jacobi theory for nonholonomic systems,
and Lagrange-Dirac equations for constrained systems.
The thirteenth chapter summarizes some recent developments in analytical dynamics,
such as differential geometry,
and Lie algebras.
The first appendix provides some background on dyadics,
such as dyadic algebra,
and dyadic transformations.
The second appendix offers some elements of topology and modern analysis,
such as metric spaces,
and function spaces.
The book is intended for advanced undergraduate and graduate students in engineering,
and applied sciences who have a solid background in classical mechanics
and differential equations.
It can also serve as a reference for researchers
and practitioners who are interested in analytical dynamics
and its applications to various fields.
The book contains 128 figures
and numerous examples
Methods of Analytical Dynamics by Leonard Meirovitch is a comprehensive
treatment of analytical dynamics
that covers both classical
and modern topics
in a clear
and logical manner.
It is a valuable resource
for anyone who wants to learn more about the theory
of analytical dynamics. 29c81ba772