Related papers: Swing-Up of a Weakly Actuated Double Pendulum via …
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…
This paper considers the optimal control problem of an extended spring-loaded inverted pendulum (SLIP) model with two additional actuators for active leg length and hip torque modulation. These additional features arise naturally in…
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…
We study dynamics of a nonlinear pendulum under a periodic force with small amplitude and slowly decreasing frequency. It is well known that when the frequency of the external force passes through the value of the frequency of the…
We discuss the equation of motion of the driven pendulum and generalize it to arbitrary driving angle. The pendulum will oscillate about a stable angle other than straight down if the drive amplitude and frequency are large enough for a…
Spin precession occurs in binary black holes whose spins are misaligned with the orbital angular momentum. Otherwise, the spin configuration is constant and the subsequent binary dynamics and gravitational-wave emission are much simpler. We…
We investigate the exact dynamics of a system of two independent harmonic oscillators coupled through their angular momentum. The exact analytic solution of the equations of motion for the field operators is derived, and the conditions for…
Model order reduction in high-dimensional, nonlinear dynamical systems if often enabled through fast-slow timescale separation. One such approach involves identifying a low-dimensional slow manifold to which the state rapidly converges and…
In this paper, we concentrate on the exponential stabilization of stochastic nonlinear systems. Different from the single event-triggering mechanism in traditional deterministic/stochastic control systems, based on two stopping time…
The purpose of this article is to illustrate the role of connections and symmetries in the Wheeled Inverted Pendulum (WIP) mechanism - an underactuated system with rolling constraints - popularized commercially as the Segway, and thereby…
Models of a playground swing have been studied since the 1960s. However, in most of them, the position of the swinger is controlled directly. This simplifies the problem but hides the mechanics of torques applied to keep the swing moving in…
We propose schemes for generating spatially-separated spin entanglement in systems of two quantum dots with onsite Coulomb repulsion weakly coupled to a joint electron reservoir. An enhanced probability for the formation of spin…
In this document, we deal with the stabilization problem of slow-fast systems (or singularly perturbed Ordinary Differential Equations) at a non-hyperbolic point. The class of systems studied here have the following properties: 1) they have…
The equilibrium configuration of an engineering structure, able to withstand a certain loading condition, is usually associated with a local minimum of the underlying potential energy. However, in the nonlinear context, there may be other…
We consider a classical problem of control of an inverted pendulum by means of a horizontal motion of its pivot point. We suppose that the control law can be non-autonomous and non-periodic w.r.t. the position of the pendulum. It is shown…
We study the late time evolution of positively curved FRW models with a scalar field which arises in the conformal frame of the $R+\alpha R^{2}$ theory. The resulted three-dimensional dynamical system has two equilibrium solutions…
It is shown that an internal control based on a moving indicator function is able to stabilize the state of parabolic equations evolving in rectangular domains. For proving the stabilizability result, we start with a control obtained from…
The variable-height inverted pendulum (VHIP) model enables a new balancing strategy by height variations of the center of mass, in addition to the well-known ankle strategy. We propose a biped stabilizer based on linear feedback of the VHIP…
We study dynamics of an wheeled inverted pendulum under a proportional-integral-derivative controller on horizontal, inclined and soft surfaces. An oscillatory area and conditions of the stability for the control are shown on the phase…
With $n$-body simulations we investigate the stability of tilted circumbinary planetary systems consisting of two nonzero mass planets. The planets are initially in circular orbits that are coplanar to each other, as would be expected if…