- Title Pages
- Dedication
- Preface to Second Edition
- Preface to First Edition
- Acknowledgments
- 1 Basic Dynamics of Point Particles and Collections
- 2 Introduction to Lagrangian Mechanics
- 3 Lagrangian Theory of Constraints
- 4 Introduction to Hamiltonian Mechanics
- 5 The Calculus of Variations
- 6 Hamilton's Principle
- 7 Linear Operators and Dyadics
- 8 Kinematics of Rotation
- 9 Rotational Dynamics
- 10 Small Vibrations about Equilibrium
- 11 Central Force Motion
- 12 Scattering
- 13 Lagrangian Mechanics with Time as a Coordinate
- 14 Hamiltonian Mechanics with Time as a Coordinate
- 15 Hamilton'S Principle and Noether's Theorem
- 16 Relativity and Spacetime
- 17 Fourvectors and Operators
- 18 Relativistic Mechanics
- 19 Canonical Transformations
- 20 Generating Functions
- 21 Hamilton-Jacobi Therory
- 22 Angle‐Action Variables
- Appendix A Vector Fundamentals
- Appendix B Matrices and Determinants
- Appendix C Eigenvalue Problem with General Metric
- Appendix D The Calculus of Many Variables
- Appendix E Geometry of Phase Space
- References
- Index
Introduction to Lagrangian Mechanics
Introduction to Lagrangian Mechanics
- Chapter:
- (p.24) 2 Introduction to Lagrangian Mechanics
- Source:
- Analytical Mechanics for Relativity and Quantum Mechanics
- Author(s):
Oliver Davis Johns
- Publisher:
- Oxford University Press
This chapter argues that modern analytical mechanics began with the work of the eighteenth-century mathematicians who elaborated Newton's ideas. Without changing Newton's fundamental principles, Euler, Laplace, and Lagrange developed elegant computational methods for the increasingly complex problems to which Newtonian mechanics was being applied. The Lagrangian formulation of mechanics is merely an abstract way of writing Newton's second law. When simple Cartesian coordinates are replaced by the most general variables capable of describing the system adequately, the Lagrange equations do not change. The vector methods fail when a mechanical system is described by systems of coordinates much more general than the standard curvilinear ones. The Lagrangian method frees one from the task of keeping track of the components of force vectors and the identities of the particles upon which they act.
Keywords: modern analytical mechanics, Euler, Laplace, Lagrange, Lagrangian formulation, Cartesian coordinates
Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.
Please, subscribe or login to access full text content.
If you think you should have access to this title, please contact your librarian.
To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .
- Title Pages
- Dedication
- Preface to Second Edition
- Preface to First Edition
- Acknowledgments
- 1 Basic Dynamics of Point Particles and Collections
- 2 Introduction to Lagrangian Mechanics
- 3 Lagrangian Theory of Constraints
- 4 Introduction to Hamiltonian Mechanics
- 5 The Calculus of Variations
- 6 Hamilton's Principle
- 7 Linear Operators and Dyadics
- 8 Kinematics of Rotation
- 9 Rotational Dynamics
- 10 Small Vibrations about Equilibrium
- 11 Central Force Motion
- 12 Scattering
- 13 Lagrangian Mechanics with Time as a Coordinate
- 14 Hamiltonian Mechanics with Time as a Coordinate
- 15 Hamilton'S Principle and Noether's Theorem
- 16 Relativity and Spacetime
- 17 Fourvectors and Operators
- 18 Relativistic Mechanics
- 19 Canonical Transformations
- 20 Generating Functions
- 21 Hamilton-Jacobi Therory
- 22 Angle‐Action Variables
- Appendix A Vector Fundamentals
- Appendix B Matrices and Determinants
- Appendix C Eigenvalue Problem with General Metric
- Appendix D The Calculus of Many Variables
- Appendix E Geometry of Phase Space
- References
- Index
