Abstract
In this chapter, we lay out the foundations of Lagrangian Mechanics. We introduce the basic concepts of Lagrangian mechanical systems, namely the Lagrangian, the action, and the equations of motion, also known as the Euler–Lagrange equations. We also discuss important examples, such as the free particle, the harmonic oscillator, as well as motions in central force potentials, such as Newton’s theory of gravity and Coulomb’s electrostatic theory. Highlighting the importance of symmetries, we study integrals of motion and Noether’s theorem. As an application, we consider motions in radial potentials and, further specializing to motions in Newton’s gravitational potential, we conclude this section with a derivation of Kepler’s laws of planetary motion.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Such a system will be usually given by a consistent specification of a system of second order differential equations for the components of the curve in each local coordinate system. A typical example is (2.3).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2017 The Author(s)
About this chapter
Cite this chapter
Cortés, V., Haupt, A.S. (2017). Lagrangian Mechanics. In: Mathematical Methods of Classical Physics. SpringerBriefs in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-56463-0_2
Download citation
DOI: https://doi.org/10.1007/978-3-319-56463-0_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-56462-3
Online ISBN: 978-3-319-56463-0
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)