Related papers: One pendulum to run them all
This study shows that typical pendulum dynamics is far from the simple equation of motion presented in textbooks. A reasonably complete damping model must use nonlinear terms in addition to the common linear viscous expression. In some…
Consider a periodically forced nonlinear system which can be presented as a collection of smaller subsystems with pairwise interactions between them. Each subsystem is assumed to be a massive point moving with friction on a compact surface,…
We investigate the cosmological attractor of the minimally coupled, self-interacting phantom field with a positive energy density but negative pressure. It is proved that the phantom cosmology is rigid in the sense that there exists a…
A heuristic but pedagogical derivation is given of an explicit formula which accurately reproduces the period of a simple pendulum even for large amplitudes. The formula is compared with others in the literature.
It is shown that the attractor of an autonomous Caputo fractional differential equation of order $\alpha\in(0,1)$ in $\mathbb{R}^d$ whose vector field has a certain triangular structure and satisfies a smooth condition and dissipativity…
The aim of this work is to extend Beno\^it's theorem for the generic existence of "canards" solutions in singularly perturbed dynamical systems of dimension three with one fast variable to those of dimension four. Then, it is established…
Context. Turbulent convection models in nonlinear radial stellar pulsation models rely on an extra equation for turbulent kinetic energy and fail to adequately explain mode-selection problems. Since multidimensional calculations are…
Based on the double pendulum and Lagrange equation, the moving particles are captured by a binocular three-dimensional capture camera. Two trajectory models of Astrojax and the relationship between trajectory empirical formula and…
A new derivation of the acceleration of a particle in a non-inertial reference frame, including the Coriolis effect, is developed using the geometry of complex numbers in the complex plane.
We investigate the dynamics of a three-dimensional system modeling a molecular mechanism for the circadian rhythm in Drosophila. We first prove the existence of a compact attractor in the region with biological meaning. Under the assumption…
Based on both qualitative method and numerical tests for a series of particular cases in the parameter region, a=1, 0<b <1, it is shown that the three-dimensional system (2) may have a series of interesting phenomena on the non-trivial…
A liquid meniscus, a bending rod (also called elastica) and a simple pendulum are all described by the same non-dimensional equation. The oscillatory regime of the pendulum corresponds to buckling rods and pendant drops, and the…
A unified, consistent and simple view of the Faraday law of induction is presented, which consists of two points: discriminating the lab- from the rest-frame electric field and understanding it is the impossibility for both fields to vanish…
In order to shed some light in the meaning of the relativistic multipolar expansions we consider different static solutions of the axially symmetric vacuum Einstein equations that in the non relativistic limit have same Newtonian moments.…
In a dissipative system, there exists the (global) attractor which has finite fractal dimensions. The flow on the attractor can be parametrized by a finite number of parameters (Temmam 1987). Using machine learning we demonstrate how to…
We present a comprehensive mechanism for the emergence of rotational horseshoes and strange attractors in a class of two-parameter families of periodically-perturbed differential equations defining a flow on a three-dimensional manifold.…
The main objective of this paper is to study the existence of a finite dimension global attractor for the three dimensional viscous primitive equations of large-scale atmosphere. Thanks to the shortage of the uniqueness of weak solutions,…
In this paper, for nonautonomous dynamical systems, we give first general conditions ensuring that a pullback attractor is a forward attractor as well in both the single and multivalued frameworks. In particular, we consider asymptotically…
The mathematical pendulum is traditionally solved using a Jacobi elliptic functions. We solve it here using the Weierstrass elliptic function. Every initial condition of the pendulum produces an elliptic curve and a point which by the…
Pendulums are simple mechanical systems that have been studied for centuries and exhibit many aspects of modern dynamical systems theory. In particular, the double pendulum is a prototypical chaotic system that is frequently used to…