On the Lagrangian and Hamiltonian description of the damped linear harmonic oscillator
From MaRDI portal
Publication:3442240
DOI10.1063/1.2711375zbMath1137.70344arXivnlin/0611048OpenAlexW3099351191MaRDI QIDQ3442240
V. K. Chandrasekar, Murugaian Senthilvelan, Muthusamy Lakshmanan
Publication date: 16 May 2007
Published in: Journal of Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/nlin/0611048
Hamilton's equations (70H05) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Lagrange's equations (70H03)
Related Items (21)
Nonlinear wave equation in an inhomogeneous medium from non-standard singular Lagrangians functional with two occurrences of integrals ⋮ Hamiltonian and Lagrangian theory of viscoelasticity ⋮ The inverse problem of a mixed Liénard-type nonlinear oscillator equation from symmetry perspective ⋮ Noether theorem and its inverse for nonlinear dynamical systems with nonstandard Lagrangians ⋮ Geometric approach to dynamics obtained by deformation of time-dependent Lagrangians ⋮ Time-independent Hamiltonians describing systems with friction: the “cyclotron with friction” ⋮ New conservation forms and Lie algebras of Ermakov-Pinney equation ⋮ Multiplication of distributions in a linear gain and loss system ⋮ Conservation laws for systems of non-standard Birkhoffians with fractional derivatives ⋮ Non-standard fractional Lagrangians ⋮ Non-standard Birkhoffian dynamics and its Noether's theorems ⋮ Generalized Hamiltonian forms of dissipative mechanical systems via a unified approach ⋮ A no-go result for the quantum damped harmonic oscillator ⋮ Nonstandard conserved Hamiltonian structures in dissipative/damped systems: Nonlinear generalizations of damped harmonic oscillator ⋮ A group theoretical identification of integrable equations in the Liénard-type equation ẍ+f(x)ẋ+g(x)=. II. Equations having maximal Lie point symmetries ⋮ Note on the Poisson structure of the damped oscillator ⋮ Quantum integrals of motion for variable quadratic Hamiltonians ⋮ A Hamiltonian yielding damped motion in an homogeneous magnetic field: quantum treatment ⋮ Comment on “On the Lagrangian and Hamiltonian description of the damped linear harmonic oscillator” [J. Math. Phys. 48, 032701 (2007)] ⋮ Quantum, noncommutative and MOND corrections to the entropic law of gravitation ⋮ A generalization of the Lagrange–Hamilton formalism with application to non-conservative systems and the quantum to classical transition
Cites Work
- Unnamed Item
- The damped harmonic oscillator in deformation quantization
- One-dimensional autonomous systems and dissipative systems
- Approach to the quantum evolution for underdamped, critically damped, and overdamped driven harmonic oscillators using unitary transformation
- Quantum damped oscillator. II: Bateman's Hamiltonian vs. 2D parabolic potential barrier
- Velocity quantization approach of the one-dimensional dissipative harmonic oscillator
- A simple and unified approach to identify integrable nonlinear oscillators and systems
- On the complete integrability and linearization of nonlinear ordinary differential equations. II. Third-order equations
- On the quantization of linearly damped harmonic oscillator
- Solving second-order ordinary differential equations by extending the Prelle-Singer method
- Quantizing the damped harmonic oscillator
- Quantum mechanics of damped systems. II. Damping and parabolic potential barrier
- Dissipation and quantization
- The quantum damped harmonic oscillator
This page was built for publication: On the Lagrangian and Hamiltonian description of the damped linear harmonic oscillator