相关论文: Nonlinear Dynamics of the 3D Pendulum

We investigate the dynamics of a single deformable self-propelled particle which undergoes a spinning motion in a two-dimensional space. Equations of motion are derived from the symmetry argument for three kinds of variables. One is a…

A physical pendulum with variable point of suspension (and, as an outcome, variable inertia moment) is experimentally analysed. In particular, the period of the small oscillations as a function of position of the suspension point is…

This paper presents a novel type of mobile rolling robot designed as a modular platform for non-prehensile manipulation, highlighting the associated control challenges in achieving balancing control of the robotic system. The developed…

In the present work, we analyzed theoretically and experimentally the nonlinear dynamics of a magnetic pendulum excited through the interactions of a strong neodymium magnet and two coils placed symmetrically around the zero angular…

A mathematical model featuring the motion of a multilink wheeled vehicle is developed using a nonholonomic model. A detailed analysis of the inertial motion is made. Fixed points of the reduced system are identified, their stability is…

We consider the motion of a planar rigid body in a potential flow with circulation and subject to a certain nonholonomic constraint. This model is related to the design of underwater vehicles. The equations of motion admit a reduction to a…

Inspired by the experimental results of Cuevas et al. (Physical Review Letters 102, 224101 (2009)), we consider theoretically the behavior of a chain of planar rigid pendulums suspended in a uniform gravitational field and subjected to a…

The results of our study of the motion of a three particle, self-gravitating system in general relativistic lineal gravity is presented for an arbitrary ratio of the particle masses. We derive a canonical expression for the Hamiltonian of…

We perform a numerical analysis of the effects of a nonlinear perturbation on the quantum dynamics of two models describing non-interacting cold atoms in a standing wave of light with a periodical modulated amplitude $A(t)$. One model is…

Control of compliant mechanical systems is increasingly being researched for several applications including flexible link robots and ultra-precision positioning systems. The control problem in these systems is challenging, especially with…

The regular or chaotic dynamics of an analytical realistic three dimensional model composed of a spherically symmetric central nucleus, a bar and a flat disk is investigated. For describing the properties of the bar we introduce a new…

Astrophysical discs which are sufficiently massive and cool are linearly unstable to the formation of axisymmetric structures. In practice, linearly stable discs of surface density slightly below the threshold needed for this instability…

In this article we discuss the effect of curvature on dynamics when a physical system moves adiabatically in a curved space. These effects give a way to measure the curvature of the space intrinsically without referring to higher…

A solution of the n-body problem in R^d is a relative equilibrium if all of the mutual distance between the bodies are constant. In other words, the bodies undergo a rigid motion. Here we investigate the possibility of partially rigid…

An inverted planar pendulum with horizontally moving pivot point is considered. It is assumed that the law of motion of the pivot point is given and the pendulum is moving in the presence of dry friction. Sufficient conditions for the…

Due to the complexity of the human body and its neuromuscular stabilization, it has been challenging to efficiently and accurately predict human motion and capture posture while being driven. Existing simple models of the seated human body…

To develop a minimal model for a cell moving in a crowded environment such as in tissue, we investigate the response of a liquid drop of active matter moving on a flat rigid substrate to forces applied at its boundaries. We consider two…

Invariant manifolds are the skeleton of the chaotic dynamics in Hamiltonian systems. In Celestial Mechanics, for instance, these geometrical structures are applied to a multitude of physical and practical problems, such as to the…

The Looping pendulum phenomenon was first introduced in 2019 at the 32nd edition of the IYPT, wherein a lighter bob sweeps around a cylindrical rod to support the weight of a heavier bob. In this paper, the phenomenon was divided based on…

The presence of physical systems whose characteristics change in a seemingly erratic manner gives rise to the study of chaotic systems. The characteristics of these systems are due to their hypersensitivity to changes in initial conditions.…