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# Advanced Dynamics

By Shuh-Jing (Benjamin) Ying

List of chapters available

Review of Fundamental Principles

Kinematics and Dynamics of a Particle

Dynamics of a System of Particles

Lagrange's Equations and the Variational Principle

Matrices, Tensors, Dyadics, and Rotation Operators

Fundamentals of Small Oscillations

Vibration of Systems with Multiple

Degrees of Freedom

Book Details

The text covers all the essential mathematical tools needed to analyze the dynamics of systems: vector algebra, conversion of coordinates, calculus of variations, matrix algebra, Cartesian tensors and dyadics, rotation operators, Fourier series, Fourier integrals, Fourier transforms, and Laplace transforms (in Chapters 1, 6, and 8). Chapters 1 through 3 start with a review of elementary statics and dynamics, followed by a discussion of Newton's laws of motion, D'Alembert's principle, virtual work, and kinematics and dynamics of a single particle or system of particles. Chapter 4 introduces Lagrange's equations and the variational principle used in dynamics. Chapter 5 is devoted to the dynamics of rockets and space vehicles, while Chapters 7, 8, and 9 discuss the dynamics of a rigid body and vibrations of continuous systems as well as lumped parameter systems with a single degree or multiple degrees of freedom. Nonlinear vibrations are also included. Chapter 10 discusses the Special Theory of Relativity and its consequences in kinematics and dynamics.