scholarly journals UPOsHam: A Python package for computing unstable periodic orbits in two-degree-of-freedom Hamiltonian systems

2020 ◽  
Vol 5 (45) ◽  
pp. 1684 ◽  
Author(s):  
Wenyang Lyu ◽  
Shibabrat Naik ◽  
Stephen Wiggins
Keyword(s):  
Periodic Orbits ◽  
Hamiltonian Systems ◽  
Degree Of Freedom ◽  
Unstable Periodic Orbits ◽  
Two Degree Of Freedom ◽  
Python Package

Analytical Stability Improvement of the Periodic Vibro-Impact Processes

1999 ◽  
Author(s):  
Jan Awrejcewicz ◽  
Krzysztof Tomczak
Keyword(s):  
Periodic Orbits ◽  
Periodic Motion ◽  
Feedback Loop ◽  
Degree Of Freedom ◽  
Loop Control ◽  
Analytical Stability ◽  
Impact Processes ◽  
Delay Loop ◽  
Sufficient Stability ◽  
Two Degree Of Freedom

Abstract In this paper an attention is focused on stabilisation improvement of periodic orbits of a one- and two-degree-of-freedom nonautonomous vibro-impact systems. This approach, among others, includes two problems. 1. A possibility of a sufficient stability improvement of the considered vibro-impact periodic motion using a feedback loop control is presented. 2. An original analytical averaging technique applied to a one-degree-of-freedom system is demonstrated. It enables to predict the efficient delay loop coefficients in order to achieve the desired stabilisation. In addition, an efficient delay loop control applied to two-degree-of-freedom system is proposed and illustrated.

scholarly journals PULSATING FEEDBACK CONTROL FOR STABILIZING UNSTABLE PERIODIC ORBITS IN A NONLINEAR OSCILLATOR WITH A NONSYMMETRIC POTENTIAL

2007 ◽  
Vol 17 (08) ◽  
pp. 2797-2803 ◽  
Author(s):  
G. LITAK ◽  
M. ALI ◽  
L. M. SAHA
Keyword(s):  
Feedback Control ◽  
Periodic Orbits ◽  
Efficient Method ◽  
Chaotic Attractor ◽  
Nonlinear Oscillator ◽  
Chaos Control ◽  
Degree Of Freedom ◽  
Unstable Periodic Orbits ◽  
Periodic State

We examine a strange chaotic attractor and its unstable periodic orbits in case of one-degree of freedom nonlinear oscillator with nonsymmetric potential. We propose an efficient method of chaos control stabilizing these orbits by a pulsating feedback technique. Discrete set of pulses enable us to transfer the system from one periodic state to another.

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