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ORIGINAL PAPER
Complex dynamics of a heavy symmetrical gyroscope under a parametric nonlinear damping
1
Physique, Chimie et Technologie, Ecole Normale Supérieure de Natitingou
2
Génie Rurale, Ecole de Génie Rural, Université Nationale d'Agriculture, Kétou, Bénin
3
Laboratoire de Mécanique des Fluides, de la Dynamique Nonlinéaire et de la Modélisation des Systèmes Biologiques, Institut de Mathématiques et de Sciences Physiques, Bénin
These authors had equal contribution to this work
Submission date: 2024-06-25
Final revision date: 2024-10-31
Acceptance date: 2024-12-15
Online publication date: 2025-03-06
Publication date: 2025-03-06
Corresponding author
International Journal of Applied Mechanics and Engineering 2025;30(1):112-126
KEYWORDS
TOPICS
ABSTRACT
This paper analyzes the chaos and coexistence of attractors of a heavy gyroscope with parametric nonlinear damping. After having found the mathematical model of the dynamics, we used the multiple scale technique to look for secondary resonances. Subsequently, the amplitude of the harmonic oscillations is determined based on the harmonic balance technique. Impact of each of the system parameters is analyzed on the amplitudes and frequency of resonances. By applying order four Runge-Kutta algorithm, the different dynamics of the gyroscope are determined and analyzed. Subharmonic resonances and harmonic oscillations are derived from the limited development the basic equation solved numerically to investigate the dynamics and coexistence of the gyroscope attractors. The analysis of impact of each parameter on the existence and disappearance of coexisting attractors is done numerically.
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