Pendulums are simple mechanical systems that have been studied for centuries and exhibit many aspects of modern dynamical theory. In particular, the double pendulum is a prototypical chaotic system frequently used to illustrate variety phenomena in nonlinear dynamics. this work, we explore existence implications codimension-1 invariant manifolds pendulum, which originate from unstable periodic ...

This thesis explores pattern evocation and energy-momentum integration of the double spherical pendulum. Pattern evocation is a phenomenon where patterns emerge when the ow of a dynamical system is viewed in a frame that rotates relative to the inertial frame. Energy-momentum integration integrates the equations of motion and exactly preserves energy and momentum at each time step. The thesis b...

The problem of mathematical modelling and indication properties a DIP has been investigated in this paper. aim work is to aggregate the knowledge on using Euler-Lagrange formalism presence external forces friction. To indicate main important for simulation, model parameters identification control system synthesis, analytical numerical tools have used. include stability equilibrium points, chaos...

A Furuta pendulum is a serial connection of two thin, rigid links, where the first link is actuated by a vertical control torque while it is constrained to rotate in a horizontal plane; the second link is not actuated. The second link of the conventional Furuta pendulum is constrained to rotate in a vertical plane orthogonal to the first link, under the influence of gravity. Methods of geometri...

The challenge in the swing-up problem of double inverted pendulum on a cart (DIPC) is to design a controller that bring all DIPC's states, especially the joint angles of the two links, into the region of attraction of the desired equilibrium. This paper proposes a new method to swing-up DIPC based on a series of restto-rest maneuvers of the first link about its vertically upright configuration ...