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Dissipation in Lagrangian Formalism.

András Szegleti1, Ferenc Márkus1

  • 1Department of Physics, Budapest University of Technology and Economics, 1111 Budapest, Hungary.

Entropy (Basel, Switzerland)
|December 8, 2020
PubMed
Summary
This summary is machine-generated.

This study introduces a new Lagrangian method for describing dissipative systems using differential equations. It simplifies modeling by generating physical quantities from a potential function, akin to electrodynamics.

Keywords:
Hamiltonian mechanicsLagrangian frameworkLagrangian mechanicscalculus of variationsdissipationharmonic oscillator

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Area of Science:

  • Physics
  • Theoretical Physics
  • Lagrangian Mechanics

Background:

  • Dissipative systems are typically challenging to model within Lagrangian formalism.
  • Existing methods often require complex environmental modeling.
  • Lagrangian mechanics is a fundamental framework in classical and quantum physics.

Purpose of the Study:

  • To present a novel method for describing dissipative systems in Lagrangian formalism.
  • To simplify the modeling of dissipative systems by avoiding explicit environmental representation.
  • To introduce a potential-based approach for generating measurable physical quantities.

Main Methods:

  • Developed a method to describe dissipative systems using linear differential equations.
  • Introduced a function that generates measurable physical quantities, analogous to scalar and vector potentials in electrodynamics.
  • Applied and examined the method within the classical physics domain.

Main Results:

  • Successfully formulated a Lagrangian description for dissipative systems.
  • The proposed method bypasses the need for explicit environmental modeling.
  • Demonstrated the generation of physical quantities from a potential function.

Conclusions:

  • The presented method offers a simplified approach to modeling dissipative systems in Lagrangian mechanics.
  • The analogy with electrodynamics provides a new perspective on potential functions in physics.
  • The quantization of this system remains an open question for future research.