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Lagrangian Mechanics

  • Vicente CortésEmail author
  • Alexander S. Haupt
Chapter
  • 1.3k Downloads
Part of the SpringerBriefs in Physics book series (SpringerBriefs in Physics)

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.

Keywords

Angular Momentum Lagrange Equation Order Differential Equation Summation Convention Convention Einstein Summation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© The Author(s) 2017

Authors and Affiliations

  1. 1.Department of Mathematics and Center for Mathematical PhysicsUniversity of HamburgHamburgGermany

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