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Phase Plane and Phase Space

In: Ordinary Differential Equations and Mechanical Systems

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  • Jan Awrejcewicz

    (Łódź University of Technology, Department of Automation, Biomechanics and Mechatronics)

Abstract

A dynamical state of an autonomous system is completely determined by the generalized coordinates y i (t) and the generalized velocities ẏ i ( t ) $$\dot{y}_{i}(t)$$ (i = 1, 2, …, n, where n is the number of degrees of freedom). Treating time t as a parameter, a point of the coordinates ( y i , ẏ i ) $$(y_{i},\dot{y}_{i})$$ will be a point of 2n-dimensional phase space. Motion of this point describes a phase trajectory as time increases. In the case of n = 1 a vibrating system has one degree-of-freedom and the phase space reduces to the phase plane.

Suggested Citation

  • Jan Awrejcewicz, 2014. "Phase Plane and Phase Space," Springer Books, in: Ordinary Differential Equations and Mechanical Systems, edition 127, chapter 0, pages 295-327, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-07659-1_9
    DOI: 10.1007/978-3-319-07659-1_9
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