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Related Experiment Video

Updated: May 18, 2026

Corticospinal Excitability Modulation During Action Observation
12:33

Corticospinal Excitability Modulation During Action Observation

Published on: December 31, 2013

Mixed convolved action.

G F Dargush1, J Kim

  • 1Department of Mechanical and Aerospace Engineering University at Buffalo, State University of New York, Buffalo, New York 14260, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 26, 2012
PubMed
Summary
This summary is machine-generated.

A new stationary principle for dynamical systems is introduced using mixed convolved action. This method unifies conservative and non-conservative systems, providing governing equations and initial conditions from a single functional.

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Area of Science:

  • Mechanical Engineering
  • Applied Mathematics
  • Fractional Calculus

Background:

  • Variational approaches traditionally struggle to unify conservative and non-conservative dynamical systems.
  • Existing methods often require separate treatments for different types of system dynamics.

Purpose of the Study:

  • To develop a unified stationary principle for dynamical systems.
  • To formulate a novel concept of mixed convolved action.
  • To incorporate fractional calculus into the variational framework for dynamics.

Main Methods:

  • Formulation of mixed convolved action using temporal convolutions and fractional derivatives.
  • Application to a canonical single-degree-of-freedom dynamical system.
  • Derivation of Euler-Lagrange equations from the stationarity of the mixed convolved action.

Main Results:

  • A single real scalar functional yields governing differential equations and initial conditions.
  • The framework successfully incorporates both conservative and non-conservative dynamical processes.
  • New results in fractional calculus relevant to dynamical systems are established.

Conclusions:

  • The developed stationary principle offers a unified approach to dynamical systems.
  • This formulation overcomes limitations of traditional variational methods.
  • The work provides a powerful new tool for analyzing complex dynamical behaviors.