Related papers: Nonlinear Dynamics of the 3D Pendulum
In this paper, we propose a nonlinear control strategy for swinging up a pendulum to its upright equilibrium position by shaping its swinging energy along with regulating the cart to a desired location. While the base of a usual cart-pole…
This paper introduces a simulation study of fluid actuated multi-driven closed system as spherical mobile robot called "RollRoller". Robot's mechanism design consists of two essential parts: tubes to lead a core and mechanical controlling…
With the aim of studying the nonlinear stellar and gaseous response to the gravitational potential of a galaxy such as the Milky Way, we have modeled 3D galactic spiral arms as a superposition of inhomogeneous oblate spheroids and added…
The purpose of the present work is to show that an adequate basis for understanding the essentially nonlinear phenomena must also be essentially nonlinear however still simple enough to play the role of a basis. It is shown that such types…
A Swinging Atwood Machine (SAM) is built and some experimental results concerning its dynamic behaviour are presented. Experiments clearly show that pulleys play a role in the motion of the pendulum, since they can rotate and have…
This study investigates the complex nonlinear coupling of magnetic gears arranged in proximity on a plane. Acknowledging the rich array of geometric and electromagnetic parameters involved, we initiate our exploration with a simplified…
The motion of a pendulum is described as Simple Harmonic Motion (SHM) in case the initial displacement given is small. If we relax this condition then we observe the deviation from the SHM. The equation of motion is non-linear and thus…
We study the most general form of a three dimensional classical integrable system with axial symmetry and invariant under the axis reflection. We assume that the three constants of motion are the Hamiltonian, $H$, with the standard form of…
In this paper, is used the Lagrangian classical mechanics for modeling the dynamics of an underactuated system, specifically a rotary inverted pendulum that will have two equations of motion. A basic design of the system is proposed in…
This paper presents a general formulation of equations of motion of a pendulum with n point mass by use of two different methods. The first one is obtained by using Lagrange Mechanics and mathematical induction(inspection), and the second…
We consider a beam model representing the transverse deflections of a one dimensional elastic structure immersed in an axial fluid flow. The model includes a nonlinear elastic restoring force, with damping and non-conservative terms…
In the classical one-dimensional solution of fluid dynamics equations all unknown functions depend only on time t and Cartesian coordinate x. Although fluid spreads in all directions (velocity vector has three components) the whole picture…
We consider model of a complex particle that consists of a rigid shell and a nucleus with spatial asymmetric interaction. The particle's dynamics with the nucleus driven by a periodic excitation is considered. It is shown that…
A spherical robot has many practical advantages as the entire electronics are protected within a hull and can be carried easily by any Unmanned Aerial Vehicle (UAV). However, its use is limited due to finding mounts for sensors. Pendulum…
This study investigates the dynamics of a magnetic pendulum under time-varying magnetic excitation with a position-dependent phase. The system exhibits complex chaotic and regular dynamics, validated through simulations and experiments. The…
Most of the advanced control systems use sensor-based feedback for robust control. Tilt angle estimation is key feedback for many robotics and mechatronics applications in order to stabilize a system. Tilt angle cannot be directly measured…
The invariant manifold approach is used to explore the dynamics of a nonlinear rotor, by determining the nonlinear normal modes, constructing a reduced order model and evaluating its performance in the case of response to an initial…
The dynamical evolution of collisionless particles in an expanding background is described. After discussing qualitatively the key features, the gravitational clustering of collisionless particles in an expanding universe is modelled using…
The majority of investigations characterizing the motion of single or multiple particles in fluid flows consider canonical body shapes, such as spheres, cylinders, discs, etc. However, protrusions on bodies -- being either as surface…
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,…