A Phase-Plane Analysis of Stability in Transient States

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概要

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• A transient process of a dynamical system is discussed in the phase plane R^2. To each pair of vectors x_1 and x_2 in R^2, their distance is introduced by the use of a positive definite symmetric matrix. To discriminate whether two trajectories passing through a neighborhood of a point x are approaching each other at that point of time or not, a repulsion rate D(x) is introduced; they are approaching each other if D(x) < 0 and going away from each other if D(x) > 0. A mathematical expression of the repulsion rate D(x) is given. Two properties of the inflector, which consists of trajectories and singular points, in relation to the repulsion rate D(x) are found. A global property such as orbital stability is discussed in terms of the repulsion rate D(x).

• 理論物理学刊行会の論文
• 1982-07-25

著者

• Okuda Masami

  Department Of Food Science And Technology Kyoto University

• Okuda Masami

  Department Of General Education Osaka Institute Of Technology

• Okuda Masami

  Department of Chemistry, Faculty of Science and Technology, Keio University

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