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Energy–vector method in mechanical oscillations

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  • Dabrowski, Artur

Abstract

The new conception of the space, and its construction are introduced. The space allows for a geometrical view on energy changes in mechanical vibrating systems. It posses all the possibilities of the system dynamics analysis that are used in the traditional phase space but it also shows an amount of the energy accumulated in the system, an energy changes, flow, dissipation, synchronization, an energy attractors. Thus it increases our knowledge and intuition on energy changes in vibrating systems. Dynamics of the chaotic system is studied using the energy space. New types of maps are introduced.

Suggested Citation

  • Dabrowski, Artur, 2009. "Energy–vector method in mechanical oscillations," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1684-1697.
    • Handle: RePEc:eee:chsofr:v:39:y:2009:i:4:p:1684-1697
    DOI: 10.1016/j.chaos.2007.06.096
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    References listed on IDEAS

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    1. Stefanski, Andrzej & Dabrowski, Artur & Kapitaniak, Tomasz, 2005. "Evaluation of the largest Lyapunov exponent in dynamical systems with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 23(5), pages 1651-1659.
    2. Dabrovski, Artur, 2005. "The construction of the energy space," Chaos, Solitons & Fractals, Elsevier, vol. 26(5), pages 1277-1292.
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