Analytical Mechanics : Solutions to Problems in Classical Physics book cover
1st Edition

Analytical Mechanics
Solutions to Problems in Classical Physics

ISBN 9781482239393
Published August 26, 2014 by CRC Press
456 Pages 122 B/W Illustrations

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Book Description

Giving students a thorough grounding in basic problems and their solutions, Analytical Mechanics: Solutions to Problems in Classical Physics presents a short theoretical description of the principles and methods of analytical mechanics, followed by solved problems. The authors thoroughly discuss solutions to the problems by taking a comprehensive approach to explore the methods of investigation. They carefully perform the calculations step by step, graphically displaying some solutions via Mathematica® 4.0.

This collection of solved problems gives students experience in applying theory (Lagrangian and Hamiltonian formalisms for discrete and continuous systems, Hamilton-Jacobi method, variational calculus, theory of stability, and more) to problems in classical physics. The authors develop some theoretical subjects, so that students can follow solutions to the problems without appealing to other reference sources. This has been done for both discrete and continuous physical systems or, in analytical terms, systems with finite and infinite degrees of freedom. The authors also highlight the basics of vector algebra and vector analysis, in Appendix B. They thoroughly develop and discuss notions like gradient, divergence, curl, and tensor, together with their physical applications.

There are many excellent textbooks dedicated to applied analytical mechanics for both students and their instructors, but this one takes an unusual approach, with a thorough analysis of solutions to the problems and an appropriate choice of applications in various branches of physics. It lays out the similarities and differences between various analytical approaches, and their specific efficiency.

Table of Contents

Fundamentals of Analytical Mechanics
Classification Criteria for Constraints
The Fundamental Dynamical Problem for a Constrained Particle
System of Particles Subject to Constraints
Lagrange Equations of the First Kind

Elementary Displacements
Real, Possible and Virtual Displacements

Virtual Work and Connected Principles
Principle of Virtual Work
Principle of Virtual Velocities
Torricelli’s Principle

Principles of Analytical Mechanics
D’alembert’s Principle
Configuration Space
Generalized Forces
Hamilton’s Principle

The Simple Pendulum Problem
Classical (Newtonian) Formalism
Lagrange Equations of the first Kind Approach
Lagrange Equations of the Second Kind Approach
Hamilton’s Canonical Equations Approach
Hamilton-Jacobi Method
Action-Angle Variables Formalism

Problems Solved by Means of the Principle of Virtual Work

Problems of Variational Calculus
Elements of Variational Calculus
Functionals. Functional Derivative
Extrema of Functionals

Problems whose solutions demand elements of variational calculus
Brachistochrone problem
Catenary problem
Isoperimetric problem
Surface of revolution of minimum area
Geodesics of a Riemannian manifold

Problems Solved by Means of the Lagrangian Formalism
Atwood machine
Double Atwood Machine
Pendulum with Horizontally Oscillating Point of Suspension
Problem of Two Identical Coupled Pendulums
Problem of Two Different Coupled Pendulums
Problem of Three Identical Coupled Pendulums
Problem of Double Gravitational Pendulum

Problems of Equilibrium and Small Oscillations

Problems Solved By Means of the Hamiltonian Formalism

Problems of Continuous Systems
A. Problems of Classical Electrodynamics
B. Problems of Fluid Mechanics
C. Problems of Magnetofluid Dynamics and Quantum Mechanics


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Author - Ioan  Merches

Ioan Merches

Emeritus Professor, Al.I.Cuza University

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