An Introduction to Lagrangian Mechanics

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World Scientific, 2008 - Science - 259 pages
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An Introduction to Lagrangian Mechanics begins with a proper historical perspective on the Lagrangian method by presenting Fermat's Principle of Least Time (as an introduction to the Calculus of Variations) as well as the principles of Maupertuis, Jacobi, and d'Alembert that preceded Hamilton's formulation of the Principle of Least Action, from which the Euler–Lagrange equations of motion are derived. Other additional topics not traditionally presented in undergraduate textbooks include the treatment of constraint forces in Lagrangian Mechanics; Routh's procedure for Lagrangian systems with symmetries; the art of numerical analysis for physical systems; variational formulations for several continuous Lagrangian systems; an introduction to elliptic functions with applications in Classical Mechanics; and Noncanonical Hamiltonian Mechanics and perturbation theory.This textbook is suitable for undergraduate students who have acquired the mathematical skills needed to complete a course in Modern Physics.
 

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Contents

The Calculus of Variations
1
Lagrangian Mechanics
35
Hamiltonian Mechanics
73
Motion in a CentralForce Field
95
Collisions and Scattering Theory
119
Motion in a NonInertial Frame
141
Rigid Body Motion
159
NormalMode Analysis
187
Continuous Lagrangian Systems
203
Appendix A Basic Mathematical Methods
217
Appendix B Elliptic Functions and Integrals
229
Noncanonical Hamiltonian Mechanics
245
Bibliography
255
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