Related papers: Analysis on the Foucault pendulum by De Alembert P…

Using the Hamiltonian formulation, we have attempted to obtain the equations of motion of systems with internal angular momentum that are moving with respect to a reference system when subjected to an interaction. This interaction involves…

In this paper we present a study of the non-linear effects of anharmonicity of the potential of the simple pendulum. In a theoretical reminder we highlight that anharmonicity of the potential generates additional harmonics and the…

For the system of an inverted spherical pendulum with friction and a periodically moving pivot point we prove the existence of at least one periodic solution with the additional property of being falling-free. The last means that the…

The effect of noise on a rotational mode of a pendulum excited kinematically in vertical direction has been analyzed. We have shown that for a weak noise transitions from oscillations to rotations and vice versa are possible. For a moderate…

We study the rolling motion of a small solid sphere on a surface patterned rubber substrate in an external field with and without a noise. In the absence of the noise, the ball does not move below a threshold force above which it…

A 3D pendulum consists of a rigid body, supported at a fixed pivot, with three rotational degrees of freedom. The pendulum is acted on by a gravitational force. Symmetry assumptions are shown to lead to the planar 1D pendulum and to the…

We perform analytical and quantitative analysis of the motion of a non-integrable pendulum with two degrees of freedom, in which an integrable nonlinear pendulum and a harmonic oscillator are weakly coupled through a non-integrable…

We provide an exact infinite power series solution that describes the trajectory of a nonlinear simple pendulum undergoing librating and rotating motion for all time. Although the series coefficients were previously given in [V. Fair\'en,…

A deformable body can rotate even with no angular momentum, simply by changing its shape. A good example is a falling cat, how it maneuvers in air to land on its feet. Here a first principles molecular level example of the phenomenon is…

The goal of this contribution is to introduce the Hamiltonian formalism of theoretical mechanics for analysing motion in generic linear and non-linear dynamical systems, including particle accelerators. This framework allows the derivation…

We introduce a two-dimensional discrete-time dynamical system which represents the evolution of an angle and angular velocity. While the angle evolves by a fixed amount in every step, the evolution of the angular velocity is governed by a…

This paper is devoted to a detailed investigation of the perturbed pendulum-like motions of a heavy rigid body about a fixed point. Canonical variables that allow one to simplify the analysis of homoclinic and heteroclinic orbits are…

Using the damped pendulum system we introduce the averaging method to study the periodic solutions of a dynamical system with small perturbation. We provide sufficient conditions for the existence of periodic solutions with small amplitude…

This paper presents an approach to damp out the oscillatory motion of the pendulum-like hanging platform on which a robotic manipulator is mounted. To this end, moving masses were installed on top of the platform. In this paper, asymptotic…

A non-local modified gravity model with an analytic function of the d'Alembert operator is considered. This model has been recently proposed as a possible way of resolving the singularities problem in cosmology. We present an exact bouncing…

Following the formalism of Gell-Mann and Hartle, phenomenological equations of motion are derived from the decoherence functional formalism of quantum mechanics, using a path-integral description. This is done explicitly for the case of a…

We describe a mechanism for transport of energy in a mechanical system consisting of a pendulum and a rotator subject to a random perturbation. The perturbation that we consider is the product of a Hamiltonian vector field and a scalar,…

This paper presents an alternative way to the dynamic modeling of a rotational inverted pendulum using the classic mechanics known as Euler-Lagrange allows to find motion equations that describe our model. It also has a design of the basic…

Starting from the recently proposed energy-based deviational formulation for solving the Boltzmann equation [J.-P. Peraud and N. G. Hadjiconstantinou, Phys. Rev. B 84, 2011], which provides significant computational speedup compared to…

The action principle is used to derive, by an entirely algebraic approach, gauge transformations of the full vacuum-to-vacuum transition amplitude (generating functional) from the Coulomb gauge to arbitrary covariant gauges and in turn to…