DocumentCode :
1162428
Title :
On Some Periodic Solutions of the Lienard Equation
Author :
Wax, Nelson
Volume :
13
Issue :
4
fYear :
1966
fDate :
12/1/1966 12:00:00 AM
Firstpage :
419
Lastpage :
423
Abstract :
Oscillations described by the generalized Li6nard equation 
are investigated in the Liénard plane. When 
and 
are subject to certain restrictions, a number of analytic curves can be obtained in this plane which serve as bounds on solution trajectories. Piecewise connection of such bounding curves provides explicit annular regions with the property that solution trajectories on the boundary of an annulus move to the interior with increasing time, 
. The Poincaré-Bendixson theorem then guarantees that at least one periodic orbit exists within such an annulus. Particular attention is given to damping functions, 
, which are asymmetric.
are investigated in the Liénard plane. When and are subject to certain restrictions, a number of analytic curves can be obtained in this plane which serve as bounds on solution trajectories. Piecewise connection of such bounding curves provides explicit annular regions with the property that solution trajectories on the boundary of an annulus move to the interior with increasing time, . The Poincaré-Bendixson theorem then guarantees that at least one periodic orbit exists within such an annulus. Particular attention is given to damping functions, , which are asymmetric.Keywords :
Circuit theory; Contracts; Damping; Equations; Helium; Mechanical systems; Oscillators;
fLanguage :
English
Journal_Title :
Circuit Theory, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9324
Type :
jour
DOI :
10.1109/TCT.1966.1082641
Filename :
1082641
Link To Document :
