ROTATIONAL DOUBLE INVERTED PENDULUM Name: Li, Bo University of Dayton Advisor: Dr. Raúl Ordóñez The thesis deals with the stabilization control of the Rotational Double Inverted Pendulum (RDIP) System. The RDIP is an extremely nonlinear, unstable, underactuated system of high order. A mathematical model is built for the RDIP with the Euler-Lagrange (E-L) equation. A Linear Quadratic Regulator (...

A modified double inverted pendulum – modified by connecting the mass carrying the pendulum with another mass through a spring makes the general inverted pendulum become a more interesting problem. The system is defined as a linear spring connected double inverted pendulum as proposed by Hou et al. [1],[2]. The system is highly nonlinear and unstable. However, the system can be simplified to a ...

We use recent results on symplectic integration of Hamiltonian systems with constraints to construct symplectic integrators on cotangent bundles of manifolds by embedding the manifold in a linear space. We also prove that these methods are equivariant under cotangent lifts of a symmetry group acting linearly on the ambient space and consequently preserve the corresponding momentum. These result...

A non-driven double pendulum model is used to explain the principle underlying the surprising efficiency of the golf swing. The principle can be described as a parametric energy transfer between the arms and the club head due to the changing moment of inertia of the club. The transfer is a consequence of conservation of energy and angular momentum. Because the pendulum is not driven by an exter...

The French Academy units of time and length — the second and the meter — are traditionally considered independent from each other. However, it is a matter of fact that a meter simple pendulum beats virtually the second in each semi oscillation, a 'surprising' coincidence that has no physical reason. We shortly review the steps that led to the choice of the meter as the ten millionth part of the...

Participants watched a recording of the motions produced when another person wielded a pendulum. The participants’ task was to judge the heaviness of the pendulum. We found that participants were similarly adept at judging the pendulum’s heaviness as when participants wield the pendulum themselves and perceive heaviness haptically. It is hypothesized that people are able to make these visual he...

this paper presented comparison of the time specification performance between two type of controller for a Double Inverted Pendulum system. Double Inverted Pendulum is a non-linear ,unstable and fast reaction system. DIP is stable when its two pendulums allocated in vertically position and have no oscillation and movement and also inserting force should be zero. The objective is to determine th...

We characterized the chaotic motion of a damped physical double pendulum which has not been achieved previously. The results consist of scattered phase plots, fractal Poincaré sections, and positive Lyapunov exponents.

In this note, property of dichotomy and Lagrange stability of the uncertain pendulum-like systems with additional, multiplicative and H∞ uncertainty are considered, respectively. By using some results of H∞ theory the property of dichotomy and Lagrange stability of uncertain pendulum-like systems with multiple equilibria are transformed into L∞ or H∞ norm condition of some transfer functions. T...

It is well-known that a suitably designed unpowered mechanical biped robot can \walk" down an inclined plane with a steady periodic gait. The energy required to maintain the motion comes from the conversion of the biped's grav-itational potential energy as it descends. Investigation of such passive natural motions may potentially lead us to strategies useful for controlling active walking machi...