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The normal and the inverted pendulum continue to be one of the main physical models and metaphors in science. The inverted pendulum is also a classic study case in control theory. In this paper we consider a special demonstration version of…
This study introduces an analytically tractable and computationally efficient model of the legged robot dynamics associated with locomotion on a dynamic rigid surface (DRS), and develops a real-time motion planner based on the proposed…
Context: Differential rotation in stars is driven by turbulent transport of angular momentum. Aims: To measure and parametrize the non-diffusive contribution to turbulent stress, known as $\Lambda$ effect, and its quenching as a function of…
Differential analysis aims at inferring global properties of nonlinear behaviors from the local analysis of the linearized dynamics. The paper motivates and illustrates the use of differential analysis on the nonlinear pendulum model, an…
Time-delayed control in a balancing problem may be a nonsmooth function for a variety of reasons. In this paper we study a simple model of the control of an inverted pendulum by either a connected movable cart or an applied torque for which…
This work explores the potential of using differentiable simulation for learning quadruped locomotion. Differentiable simulation promises fast convergence and stable training by computing low-variance first-order gradients using robot…
The 1:1:2 resonant elastic pendulum is a simple classical system that displays the phenomenon known as Hamiltonian monodromy. With suitable initial conditions, the system oscillates between nearly pure springing and nearly pure…
We use three-dimensional hydrodynamic simulations to investigate the nonlinear gravitational responses of gas to, and the resulting drag forces on, very massive perturbers moving on circular orbits. This work extends our previous studies…
Nowadays, most studies on the dynamic properties of annular gaps focus only on the force characteristics due to translational motions, while the tilt and moment coefficients are less well studied. Therefore, there is hardly any reliable…
Models of bipedal locomotion are hybrid, with a continuous component often generated by a Lagrangian plus actuators, and a discrete component where leg transfer takes place. The discrete component typically consists of a locally embedded…
This research focuses on the interesting physical phenomenon of the bead-hoop system. The bifurcation can be observed investigating the equilibrium point of the bead, and nonlinear oscillation also occurs from the bead's motion. This paper…
The Dynamic Hubbard Model represents the physics of a multi-band Hubbard model by using a pseudo-spin degree of freedom to dynamically modify the on-site Coulomb interaction. Here we use a dimer system to obtain analytical results for this…
We study the morphological evolution of surfaces during ion sputtering and we compare their dynamical roughening with aeolian ripple formation in sandy deserts. We show that, although the two phenomena are physically different, they must…
Analyzing the motion of a roller coaster allows for an instructive introduction of various theoretical concepts in a concrete and enjoyable context. We start by modeling the roller coaster train as a point particle. We then develop more…
The wide use of a speed-independent distance as a cut-off impact parameter together with Rutherford's scattering formula, within the cut-off theory, to account for charge screening in plasma environment embodies a clear inconsistency. A new…
This paper introduces an indirect adaptive fuzzy model predictive control strategy for a nonlinear rotational inverted pendulum with model uncertainties. In the first stage, a nonlinear prediction model is provided based on the fuzzy sets,…
A recent large deflection cantilever model is considered. The principal nonlinear effects come through the beam's inextensibility---local arc length preservation---rather than traditional extensible effects attributed to fully restricted…
The space missions designed to visit small bodies of the Solar System boosted the study of the dynamics around non-spherical bodies. In this vein, we study the dynamics around a class of objects classified by us as Non-Spherical Symmetric…
Recent observational and theoretical studies indicate that the damping of solar coronal loop oscillations depends on the oscillation amplitude. We consider two mechanisms, linear resonant absorption and a nonlinear damping model. We…
An experiment is proposed which can distinguish between two approaches to the reality of the electric field, and whether it has mechanical properties such as mass and stress. A charged pendulum swings within the field of a much larger…