Introduction To Classical Mechanics By Takwale

Introduction to Classical Mechanics

An Introduction to Dynamical Systems and Chaos

The book discusses continuous and discrete systems in systematic and sequential approaches for all aspects of nonlinear dynamics. The unique feature of the book is its mathematical theories on flow bifurcations, oscillatory solutions, symmetry analysis of nonlinear systems and chaos theory. The logically structured content and sequential orientation provide readers with a global overview of the topic. A systematic mathematical approach has been adopted, and a number of examples worked out in detail and exercises have been included. Chapters 1–8 are devoted to continuous systems, beginning with one-dimensional flows. Symmetry is an inherent character of nonlinear systems, and the Lie invariance principle and its algorithm for finding symmetries of a system are discussed in Chap. 8. Chapters 9–13 focus on discrete systems, chaos and fractals. Conjugacy relationship among maps and its properties are described with proofs. Chaos theory and its connection with fractals, Hamiltonian flows and symmetries of nonlinear systems are among the main focuses of this book. Over the past few decades, there has been an unprecedented interest and advances in nonlinear systems, chaos theory and fractals, which is reflected in undergraduate and postgraduate curricula around the world. The book is useful for courses in dynamical systems and chaos, nonlinear dynamics, etc., for advanced undergraduate and postgraduate students in mathematics, physics and engineering.

Classical and Analytical Mechanics

Classical and Analytical Mechanics: Theory, Applied Examples, and Practice provides a bridge between the theory and practice related to mechanical, electrical, and electromechanical systems. It includes rigorous mathematical and physical explanations while maintaining an interdisciplinary engineering focus. Applied problems and exercises in mechanical, mechatronic, aerospace, electrical, and control engineering are included throughout and the book provides detailed techniques for designing models of different robotic, electrical, defense, and aerospace systems. The book starts with multiple chapters covering kinematics before moving onto coverage of dynamics and non-inertial and variable mass systems. Euler's dynamic equations and dynamic Lagrange equations are covered next with subsequent chapters discussing topics such as equilibrium and stability, oscillation analysis, linear systems, Hamiltonian formalism, and the Hamilton-Jacobi equation. The book concludes with a chapter outlining various electromechanical models that readers can implement and adapt themselves. - Bridges theory and practice by providing readers techniques for solving common problems through mechanical, electrical, and electromechanical models alongside the underlying theoretical foundations - Describes variable mass, non-inertial systems, dynamic Euler's equations, gyroscopes, and other related topics - Includes a broad offering of practical examples, problems, and exercises across an array of engineering disciplines