Time-Dependent Lagrangians: Reference Work & Euler-Lagrange Equations

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SUMMARY

The discussion focuses on the need for reference materials regarding time-dependent Lagrangians, specifically in the context of forced harmonic oscillators and the Euler-Lagrange equations. The participant highlights that traditional classical textbooks often overlook this area, particularly when addressing non-energy conserving systems. They emphasize the necessity of including a partial derivative with respect to time in the derivation of the Euler-Lagrange equations. The conversation suggests that applied mechanics texts, particularly those related to celestial mechanics, tokamaks, or particle accelerators, are the most suitable resources for further study.

PREREQUISITES
  • Understanding of Lagrangian mechanics
  • Familiarity with Euler-Lagrange equations
  • Knowledge of forced harmonic oscillators
  • Basic concepts of applied mechanics in physics
NEXT STEPS
  • Research applied mechanics textbooks focusing on celestial mechanics
  • Explore resources on tokamak physics and its applications
  • Study particle accelerator design and operation
  • Investigate advanced topics in time-dependent Lagrangians and their applications
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Physicists, mechanical engineers, and students studying advanced mechanics, particularly those interested in time-dependent systems and their applications in fields like particle physics and engineering.

StuckOnZero
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I'm looking for a good reference work on time-dependent Lagrangians. For example, the Lagrangian and resultant Euler-Lagrange equations for a forced harmonic oscillator. All the classical textbooks just skip over this subject area. Obviously the system is non-energy conserving. In deriving the E-L equations one has to add a partial wrt T. I am looking to solve some electron trajectory problems when there is a weak oscillating external E-field.
-Thanks
 
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Your best bet will be a book on applied mechanics, either celestial mechanics, tokamak or particle accelerators.
 

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