A Hamiltonian with a Subset of Normal Modes for Studying Mode-Specific Energy Transfer in Intermolecular Collisions†

2001 ◽  
Vol 105 (12) ◽  
pp. 2617-2625 ◽  
Author(s):  
Tianying Yan ◽  
William L. Hase
Keyword(s):  
Energy Transfer ◽  
Specific Energy ◽  
Normal Modes

scholarly journals Limiting Phase Trajectories and Resonance Energy Transfer in a System of Two Coupled Oscillators

2010 ◽  
Vol 2010 ◽  
pp. 1-24 ◽  
Author(s):  
L. I. Manevitch ◽  
A. S. Kovaleva ◽  
E. L. Manevitch
Keyword(s):  
Energy Transfer ◽  
Coupled Oscillators ◽  
Energy Exchange ◽  
Duffing Oscillator ◽  
Normal Modes ◽  
Resonance Energy ◽  
Harmonic Excitation ◽  
Conservation Of Energy ◽  
Phase Trajectories ◽  
Limiting Phase Trajectories

We study a problem of energy exchange in a system of two coupled oscillators subject to 1 : 1 resonance. Our results exploit the concept of limiting phase trajectories (LPTs). The LPT, associated with full energy transfer, is, in certain sense, an alternative to nonlinear normal modes characterized by conservation of energy. We consider two benchmark examples. As a first example, we construct an LPT and examine the convergence to stationary oscillations for a Duffing oscillator subjected to resonance harmonic excitation. As a second example, we treat resonance oscillations in a system of two nonlinearly coupled oscillators. We demonstrate the reduction of the equations of motion to an equation of a single oscillator. It is shown that the most intense energy exchange and beating arise when motion of the equivalent oscillator is close to an LPT. Damped beating and the convergence to rest in a system with dissipation are demonstrated.

Orbital-Specific Energy Transfer

2010 ◽  
Vol 132 (7) ◽  
pp. 2208-2221 ◽  
Author(s):  
Troy E. Knight ◽  
James K. McCusker
Keyword(s):  
Energy Transfer ◽  
Specific Energy

Coriolis coupling effects on energy transfer: classical-trajectories analysis for CO2 + Ar collisions

2007 ◽  
Vol 85 (11) ◽  
pp. 983-988 ◽  
Author(s):  
E Borges ◽  
J P Braga
Keyword(s):  
Energy Transfer ◽  
Initial Conditions ◽  
Normal Modes ◽  
Coriolis Coupling ◽  
Coupling Energy ◽  
Rotational States ◽  
Quantum Numbers ◽  
Classical Trajectories ◽  
Vibration Rotation ◽  
Made In

Energy transfer on CO2 + Ar collisions is studied by performing classical-trajectories simulations in a non-rigid potential-energy surface. Partition of molecular kinetic energy into vibration, rotation, and Coriolis coupling is made in a Cartesian coordinates system, coupled to vibrational normal modes. Initial atomic translational energies are selected from a range of 0.004–0.4 au, and initial molecular rotational states are fixed at rotational quantum numbers j, equal to 1, 20, 40, and 60. Effects of these different initial conditions are investigated, and the Coriolis influence on the energy transferred is analyzed.Key words: Coriolis coupling, energy, classical trajectories.

Constructing the Frequency-Energy Plot of Nonlinear Vibratory Systems via the Modified Lindstedt-Poincaré Method

2013 ◽  
Vol 655-657 ◽  
pp. 547-550
Author(s):  
Xin Hua Zhang
Keyword(s):  
Energy Transfer ◽  
Nonlinear Vibration ◽  
Normal Modes ◽  
Nonlinear Normal Modes ◽  
Numerical Results ◽  
Internal Resonances ◽  
Nonlinear Normal ◽  
Vibrating Systems

The frequency-energy plot(FEP) of nonlinear vibration systems is a powerful tool for investigating the energy transfer phenomena related wiht the internal resonances occured in multi-digreeof- freedom(Multi-DOF) nonlinear vibration systems. In this paper, the modified Lindstedt-Poincare method is employed for constructing the FEP of a two-DOF nonlinear vibrating systems. First, the original vibartion equations are modified for the application of the modified Linstedt-Poincaré method. Then, by using the modified Linstedt-Poincaé method, the nonlinear normal modes(NNMs) of the system are obtained. Finally, the frequency-energy plot of the system is constructed analytically. Numerical results show that the method adopted in this paper is effective and accurate.

Energy Transfer and Dissipation in a Duffing Oscillator Coupled to a Nonlinear Attachment

2009 ◽  
Vol 4 (4) ◽  
Author(s):  
R. Viguié ◽  
M. Peeters ◽  
G. Kerschen ◽  
J.-C. Golinval
Keyword(s):  
Energy Transfer ◽  
Hamiltonian System ◽  
Nonlinear System ◽  
Duffing Oscillator ◽  
Normal Modes ◽  
Nonlinear Normal Modes ◽  
Numerical Continuation ◽  
Damped System ◽  
Nonlinear Normal ◽  
Two Degree Of Freedom

The dynamics of a two-degree-of-freedom nonlinear system consisting of a grounded Duffing oscillator coupled to an essentially nonlinear attachment is examined in the present study. The underlying Hamiltonian system is first considered, and its nonlinear normal modes are computed using numerical continuation and gathered in a frequency-energy plot. Based on these results, the damped system is then considered, and the basic mechanisms for energy transfer and dissipation are analyzed.

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