In order to investigate the geometrical relation between two flows in two dynamical systems, a flow for an investigated dynamical system is called the compared flow and a flow for a given dynamical system is called the reference flow. A surface on which the reference flow lies is termed the reference surface. The time-change rate of the normal distance between the reference and compared flows in the normal direction of the reference surface is measured by a new function (i.e., function). Based on the surface of the reference flow, the -order functions are introduced for the noncontact and -order contact flows in two different dynamical systems. Through the new functions, the geometric relations between two flows in two dynamical systems are investigated without contact between the reference and compared flows. The dynamics for the compared flow with a contact to the reference surface is briefly addressed. Finally, the brief discussion of applications is given.
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January 2008
Research Papers
On the Differential Geometry of Flows in Nonlinear Dynamical Systems
Albert C. J. Luo
Albert C. J. Luo
Department of Mechanical and Industrial Engineering,
e-mail: aluo@siue.edu
Southern Illinois University Edwardsville
, Edwardsville, IL 62026-1805
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Albert C. J. Luo
Department of Mechanical and Industrial Engineering,
Southern Illinois University Edwardsville
, Edwardsville, IL 62026-1805e-mail: aluo@siue.edu
J. Comput. Nonlinear Dynam. Jan 2008, 3(2): 021104 (10 pages)
Published Online: March 11, 2008
Article history
Received:
May 28, 2007
Revised:
August 23, 2007
Published:
March 11, 2008
Citation
Luo, A. C. J. (March 11, 2008). "On the Differential Geometry of Flows in Nonlinear Dynamical Systems." ASME. J. Comput. Nonlinear Dynam. January 2008; 3(2): 021104. https://doi.org/10.1115/1.2835060
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