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Phase Self-Stabilization

  • N. G. Basov
Part of the The Lebedev Physics Institute Series book series (LPIS)

Abstract

If x = x0(t) is the solution of the system of equations with the initial condition x0 (t0) = a, then the condition x0 (t + γ) = a evidently corresponds to the solution x = x0(t + γ). The set of motions of an autonomous dynamic system permits arbitrary shifts in time. Solutions of the form x0 (t + γ) for arbitrary fixed values of γ are combined by the curve [x0(θ)] in {x} space by saying that the motions with a given trajectory [x0(θ)] differ only by a constant phase difference.† This concept is generalized to motion along different (nearby) trajectories. Denoting the image point of the motion x(t) on the curve [x0(θ)] by x0(t + γ(t)), γ(t) is called the phase difference between the motions x(t) and x0(t) [1, 2]. Phase considerations make it possible to explain properties of the motion associated with shifts in time, thereby easing the analysis of complicated systems.

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Copyright information

© Springer Science+Business Media New York 1978

Authors and Affiliations

  • N. G. Basov
    • 1
  1. 1.P. N. Lebedev Physics InstituteAcademy of Sciences of the USSRMoscowUSSR

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