Interaction of Nonlinear Oscillations

Mitropol’skii, Yu. A.; Dao, Nguyen Van

doi:10.1007/978-94-015-8847-8_5

Cited by 6 publications

(5 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In order to close a set of averaged equations one needs some additional relations between the variables . For instance, in the classical equivalent linearization and averaging methods one puts z(t) = x(t) [1][2][3] . Then, in these techniques, x(t) represents only a linear system while z(t) is from a nonlinear one.…”

Section: Extension Of Moment Equation Methods To Deterministic Nonlinementioning

confidence: 99%

Analysis of some nonlinear deterministic oscillators using extended averaged equation approach

Hai

2005

Vietnam J. Mech.

View full text Add to dashboard Cite

show abstract

Section: Extension Of Moment Equation Methods To Deterministic Nonlinementioning

confidence: 99%

Analysis of some nonlinear deterministic oscillators using extended averaged equation approach

Hai

2005

Vietnam J. Mech.

View full text Add to dashboard Cite

show abstract

“…An approach based on the method of averaging has been developed and applied to a wide spectrum of applications. See Bogolyubov and Mitropolskii [4], Volosov [21], and Mitropolskii and Dao [19]. The approach requires sophisticated changes of variables (that at times blur the physics behind the phenomenon).…”

Section: Introductionmentioning

confidence: 99%

The pendulum under vibrations revisited

Artstein

2021

Nonlinearity

View full text Add to dashboard Cite

A simple intuitive physical explanation is offered, of the stability of the inverted pendulum under fast violent vibrations. The direct description allows to analyze, both intuitively and rigorously, the effect of vibrations in similar, and in more general, situations. The rigorous derivations in the paper follow a singular perturbations model of mixed slow and fast dynamics. The approach allows applications beyond the classical inverted pendulum model.

show abstract

“…Yet, for large frequency shifts the dependence of frequency on temperature is usually non-linear. 9,[41][42][43][44] In the present work, we drop the linearization assumption and focus on effects induced by higher order terms in Eq. (3).…”

Section: Introductionmentioning

confidence: 99%

Heat capacities of thermally manipulated mechanical oscillator at strong coupling

Kolář

Ryabov

Filip

2019

Sci Rep

View full text Add to dashboard Cite

Coherent quantum oscillators are basic physical systems both in quantum statistical physics and quantum thermodynamics. Their realizations in lab often involve solid-state devices sensitive to changes in ambient temperature. We represent states of the solid-state optomechanical oscillator with temperature-dependent frequency by equivalent states of the mechanical oscillator with temperature-dependent energy levels. We interpret the temperature dependence as a consequence of strong coupling between the oscillator and the heat bath. We explore parameter regimes corresponding to anomalous behavior of mechanical and thermodynamic characteristics as a consequence of the strong coupling: (i) The localization and the purification induced by heating, and (ii) the negativity of two generalized heat capacities. The capacities can be used to witness non-linearity in the temperature dependency of the energy levels. Our phenomenological experimentally-oriented approach can stimulate development of new optomechanical and thermomechanical experiments exploring basic concepts of strong coupling thermodynamics.

show abstract

Interaction of Nonlinear Oscillations

Cited by 6 publications

References 0 publications

Analysis of some nonlinear deterministic oscillators using extended averaged equation approach

Analysis of some nonlinear deterministic oscillators using extended averaged equation approach

The pendulum under vibrations revisited

Heat capacities of thermally manipulated mechanical oscillator at strong coupling

Contact Info

Product

Resources

About