Experimental investigation of perpetual points in mechanical systems
P. Brzeski,Lawrence N. Virgin +1 more
TL;DR: In this article, an experimental setup is described, specifically designed to investigate perpetual points, including a description of the data analysis approaches developed to identify their location. But this paper focuses on the occurrence of these points in a simple mechanical system, including experimental verification.
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Abstract: In dissipative dynamical systems, equilibrium (stationary) points have a dominant organizing effect on transient motion in phase space, especially in nonlinear systems. These time-independent solutions are readily defined in the context of ordinary differential equations, that is, they occur when all the time derivatives are simultaneously zero. However, there has been some recent interest in perpetual points: points at which the higher time derivatives are zero, but not necessarily the first. Previous work has focused on analytic work (including simulation) and some experimental studies of electric circuits. This paper focuses attention on the occurrence of these points in a simple mechanical system, including experimental verification. Thus, points of zero acceleration can be found in which the corresponding velocity is a maximum or minimum, but not zero. Specifically, the rigid-arm pendulum is used to generate data for which acceleration (and its derivative) can be evaluated. In this paper an experimental (mechanical) setup is described, specifically designed to investigate perpetual points, including a description of the data analysis approaches developed to identify their location.
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Citations
System identification of energy dissipation in a mechanical model undergoing high velocities: An indirect use of perpetual points
P. Brzeski,Lawrence N. Virgin +1 more
TL;DR: It is shown that certain features of high-velocity, spinning motion lends itself to greater fidelity in the data-fitting process and thus added confidence in choosing the most accurate energy dissipation model with the most appropriate parameters.
14
Perpetual points in natural mechanical systems with viscous damping: A theorem and a remark:
Fotios Georgiades
- 23 Jun 2020
TL;DR: In this paper, the nature of perpetual points in natural dissipative mechanics is investigated and the role of these points in the dynamics of mechanical systems is discussed. But, their role is not discussed in this paper.
12
Theorem and observation about the nature of perpetual points in conservative mechanical systems
Fotios Georgiades
- 15 Jul 2018
TL;DR: This work is essential to understand the nature of perpetual points in mechanical systems and opens new horizons for new operational modes and new design processes, targeting the ultimate operational modes of many mechanical systems which are the rigid body motions without having any vibrations.
11
Augmented Perpetual Manifolds and Perpetual Mechanical Systems—Part I: Definitions, Theorem, and Corollary for Triggering Perpetual Manifolds, Application in Reduced-Order Modeling and Particle-Wave Motion of Flexible Mechanical Systems
TL;DR: In this article, the authors extended the definition of perpetual manifolds to the augmented perpetual manifold of rigid body motions and proved that for harmonic motion, the system moves in dual mode as wave-particle.
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New topological tool for multistable dynamical systems
TL;DR: A new method for investigation of dynamical systems which allows to extract as much information as possible about potential system dynamics, based only on the form of equations describing it and provides a better understanding of attractors geometry and their capturing in complex cases, especially including multistable and hidden attractors.
8
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