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.    Contents:  The Calculus of Variations; Lagrangian Mechanics; Hamiltonian  Mechanics; Motion in a Central-Force Field; Collisions and Scattering Theory;  Motion in a Non-Inertial Frame; Rigid Body Motion; Normal-Mode Analysis;  Continuous Lagrangian Systems;  Appendices:  ; Basic Mathematical  Methods; Elliptic Functions and Integrals; Noncanonical Hamiltonian Mechanics.

An Introduction to Lagrangian Mechanics PDF

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