Classicalmechanicsbygaruldhaspdf

[Vilma Steiert]

Classical Mechanics by G. Aruldhas: A Review

Classical mechanics is one of the fundamental branches of physics that deals with the motion of particles and systems under the influence of forces. It is also the foundation for many other fields of physics, such as electromagnetism, thermodynamics, quantum mechanics, and relativity. Therefore, a solid understanding of classical mechanics is essential for any student or researcher who wants to explore the physical world.

classicalmechanicsbygaruldhaspdf

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There are many textbooks on classical mechanics available in the market, but one of the most popular and comprehensive ones is Classical Mechanics by G. Aruldhas. This book offers an in-depth presentation of the mechanics of particles and systems, covering both the theoretical and practical aspects of the subject. The book is suitable for a one-semester course in classical mechanics for postgraduate students of physics and mathematics, as well as a useful reference for engineering students at the postgraduate level.

The book provides not only a complete treatment of classical theoretical physics but also an enormous number of worked examples and problems to show students clearly how to apply abstract principles and mathematical techniques to realistic problems. While abstraction of theory is minimized, detailed mathematical analysis is provided wherever necessary. The book also includes topics from the rapidly growing areas of nonlinear dynamics and chaos, which are relevant for many modern applications of classical mechanics.

The book consists of 12 chapters, each with a summary, a list of key points, and a set of exercises. The chapters are as follows:

• Chapter 1: Introduction: This chapter gives an overview of the scope and objectives of classical mechanics, as well as some historical background and basic concepts.

• Chapter 2: Lagrange's Equation: This chapter introduces the principle of least action and derives Lagrange's equation for holonomic systems. It also discusses some applications of Lagrange's equation, such as the conservation laws, the generalized momentum, and the Hamilton's principle.

• Chapter 3: Hamilton's Equation: This chapter derives Hamilton's equation from Lagrange's equation and introduces the concept of canonical transformation. It also discusses some applications of Hamilton's equation, such as the Poisson bracket, the Liouville's theorem, and the Hamilton-Jacobi equation.

• Chapter 4: Central Force Motion: This chapter deals with the motion of a particle under a central force field, such as the gravitational or electrostatic force. It covers topics such as the Kepler's laws, the orbital elements, the orbital transfers, and the scattering problem.

• Chapter 5: Small Oscillations: This chapter studies the motion of a system near an equilibrium position, which can be approximated by harmonic oscillations. It covers topics such as the normal modes, the normal coordinates, the matrix method, and the perturbation method.

• Chapter 6: Rigid Body Motion: This chapter analyzes the motion of a rigid body, which is a system of particles that maintain fixed distances from each other. It covers topics such as the angular velocity, the angular momentum, the inertia tensor, the Euler's angles, and the Euler's equations.

• Chapter 7: Nonlinear Dynamics: This chapter introduces some concepts and methods of nonlinear dynamics, which deals with systems that exhibit complex and chaotic behavior. It covers topics such as the phase space, the fixed points, the stability analysis, the bifurcation theory, and the Poincaré map.

• Chapter 8: Chaos: This chapter explores some examples and characteristics of chaotic systems, which are sensitive to initial conditions and unpredictable in long-term evolution. It covers topics such as the logistic map, the Lorenz system, the Rossler system, and the strange attractor.

• Chapter 9: Special Theory of Relativity: This chapter presents the basic postulates and consequences of special relativity, which is a theory that describes the motion of objects at high speeds. It covers topics such as the Lorentz transformation, the four-vectors, the relativistic kinematics, and the relativistic dynamics.

• Chapter 10: Relativistic Mechanics: This chapter extends classical mechanics to relativistic situations using Lagrangian and Hamiltonian formulations. It covers topics such as the relativistic Lagrangian and Hamiltonian functions, the relativistic action principle, the relativistic conservation laws, and the relativistic Hamilton-Jacobi equation.

• Chapter 11: Tensor Analysis: This chapter introduces some concepts and methods of tensor analysis, which is a mathematical tool for dealing with quantities that transform under coordinate transformations. It covers topics such as the tensor notation, the tensor algebra, the tensor calculus, and the metric tensor.

• Chapter 12: General Theory of Relativity: This chapter gives a brief introduction to general relativity, which is a theory that describes the motion of objects in curved spacetime. It covers topics such as the equivalence principle, the geodesic equation, the Einstein's field equation, and the Schwarzschild solution.

The book is written in a clear and concise style, with ample illustrations and examples to aid understanding. The book also provides references to other books and articles for further reading. The book is available in both print and digital formats. The digital format can be accessed through Google Books or Google Play. A PDF version of the book can also be found online, but it may not be authorized by the publisher or the author.

In conclusion, Classical Mechanics by G. Aruldhas is a comprehensive and informative textbook on classical mechanics that covers both the theoretical and practical aspects of the subject. The book is suitable for students and researchers who want to learn classical mechanics in depth and apply it to various problems. The book also includes topics from nonlinear dynamics and chaos, which are relevant for modern applications of classical mechanics. The book is highly recommended for anyone who wants to master classical mechanics.

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