1st Edition
Analytical Mechanics Solutions to Problems in Classical Physics
Fundamentals of Analytical Mechanics
Constraints
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
Generalities
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
APPENDICES
REFERENCES
Biography
Ioan Merches, Daniel Radu
