Guide Some problems in the theory of nonlinear oscillations

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Students quickly become bored if they are just passive consumers of information. They learn better when they need to respond frequently to computer software.


  1. Applied Methods In The Theory Of Nonlinear Oscillations.
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At the same time interactive software must be sufficiently structured that users do not lose sight of the educational target. You can obtain time-dependent graphs of the variables that describe the simulated system, phase diagrams and graphs of energy transformations.

Graphs and diagrams appear on the screen simultaneously with the motion display. The suggested experiments have been designed to be plain and obvious. They provide the capability of observing repeatedly and thoroughly the fine details of phenomena that usually escape notice during direct observation.

You can widely modify parameters of the investigated physical systems and conditions of the experiments. The graphic presentation of the results allows you to see and easily understand large amounts of information. The simulations bring to life many abstract concepts related to the physics of oscillations and can lead to considerable insight into the complex behavior exhibited by nonlinear systems. The programs provide the instructor with powerful demonstration tools to accompany lectures in general physics and the theory of oscillations. With these programs, the students have an opportunity to perform interesting mini-research physics projects on their own.

A high resolution screen mode x or higher is recommended. Printer is optional. Click here or on the button above to download the archive file Nonlinear.

A new dissipativity criterion—towards Yakubovich oscillations

Then unzip it to a folder on your local machine and run a standard setup procedure click on the file setup. To launch the simulation programs, click on the icon "Nonlinear Oscillations" created on your desktop by the setup procedure. We note that all programs of the package are supplied with several sets of predefined examples illustrating many interesting modes of the simulated system behavior. To open the list of examples, click on the button "Demo Examples" on the title screen, or on the menu item "Examples" which can be found in the upper line of any screen, or in the pop-up menu called by clicking the right mouse button.

We recommend to use these examples at first acquaintance with the programs. Additional background material explaining the simulated physical systems and different modes of their behavior can be found in text documents and articles pdf files that supplement almost all programs of the package.

You will need Adobe Acrobat Reader program to read papers and other text documents of the package. These materials are available directly from the programs by clicking "Help on physics" in the menu. Some of the papers have been published in the literature: Parametric Resonance. See abstract and full pdf version KB. European Journal of Physics , v.

Buchbestand Details

On the Dynamic Stabilization of an Inverted Pendulum. American Journal of Physics , v. Subharmonic Resonances of the Parametrically Driven Pendulum. Journal of Physics A: Mathematical and General , v. Square-wave excitation of a linear oscillator.

mathematics and statistics online

Parametric excitation of a linear oscillator. Parametric resonance in a linear oscillator at square-wave modulation.


  • Contributions to the Theory of Nonlinear Oscillations (AM-36), Volume III.
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  • Extraordinary oscillations of an ordinary forced pendulum. See abstract and full pdf version 1. An improved criterion for Kapitza's pendulum stability.

    Nonlinear Autonomous Oscillations: Analytical Theory, Volume 34

    Journal of Physics A: Mathematical and Theoretical , v. See full pdf version 1. Oscillations of a simple pendulum with extremely large amplitudes. The package includes a set of highly interactive programs that allow the user to observe the simulations of simple mechanical oscillatory systems, and obtain time-dependent graphs of the variables that describe the simulated system, phase diagrams and graphs of energy transformations.

    Kuzio, and M. Gornyi zhurnal [Vibrations in technique and technologies] , no.

    Averaging method in some problems of the theory of nonlinear oscillations

    Mitropol'skii, and B. Vladimirov, A. Maidanovskii, S.


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    • Novikov, Nelineinye kolebaniia mnogochastotnykh avtokolebatelnykh sistem [Nonlinear oscillations of multi-frequency self-oscillatory systems]. Tomsk, Russia: Izdatelstvo Tomskogo universiteta, Kharchenko, and M. Sokil, A. Andrukhiv, O. Sokil, and M. Goldin, Vibratciia rotornykh mashin [Vibration of rotary machines]. Moscow, Russia: Mashinostroenie Publ.