Phase Plane and Phase Space

Jan Awrejcewicz
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Jan Awrejcewicz: Łódź University of Technology, Department of Automation, Biomechanics and Mechatronics

Chapter Chapter 9 in Ordinary Differential Equations and Mechanical Systems, 2014, pp 295-327 from Springer

Abstract: 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.

Keywords: Phase Trajectories; Phase Point Approaches; Degenerate Node; Unstable Focus; Parallel Tangent Lines (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-07659-1_9

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DOI: 10.1007/978-3-319-07659-1_9

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