Related papers: Constant of Motion for One-Diemnsional Non Autonom…
For system of two ordinary differential equations of the second order representing autonomous non-conservative holonomic mechanical system, in case of dynamics such as one-frequency periodical oscillations, is found integrated invariant of…
The steady state motion of a folded pendulum has been studied using frequencies of drive that are mainly below the natural (resonance) frequency of the instrument. Although the free-decay of this mechanical oscillator appears textbook…
We study the dynamics of a mechanical oscillator with linear and cubic forces -the Duffing oscillator- subject to a feedback mechanism that allows the system to sustain autonomous periodic motion with well-defined amplitude and frequency.…
We present exact analytical solutions to the classical equations of motion and analyze the dynamical consequences of the existence of a minimal length for the free particle, particle in a linear potential, anti-symmetric constant force…
It is well-known that an electric charge under a uniform magnetic field has a bidimensional motion if its initial position and velocity are perpendicular to this magnetic field. Although some constants of motion, as the energy and angular…
We investigate the dynamics of a single deformable self-propelled particle which undergoes a spinning motion in a two-dimensional space. Equations of motion are derived from the symmetry argument for three kinds of variables. One is a…
In this article the problem for the using of uniformly rotating coordinate system is considered. The correct relations between the kinematical quantities characterizing the motion of a body relative to uniformly rotating system and static…
In this work a classical linear harmonic oscillator, evolving during a small time interval (so that simple non-linear, second order Taylor approximation of the dynamics is satisfied) and restarting (by a mechanism) in a strictly chosen…
A treatment is given of the orbit dynamics for linear unstable motion that allows for the zeros in the beta function and makes no assumptions about the realness of the betatron and phase functions. The phase shift per turn is shown to be…
In this paper, we describe a numerical continuation method that enables harmonic analysis of nonlinear periodic oscillators. This method is formulated as a boundary value problem that can be readily implemented by resorting to a standard…
Non-linear dynamical systems represent a compact, flexible, and robust tool for reactive motion generation. The effectiveness of dynamical systems relies on their ability to accurately represent stable motions. Several approaches have been…
Linear time invariant (LTI) systems are widely used for modeling system dynamics in science and engineering problems. Harmonic oscillation of LTI systems are widely used for modeling and analyses of periodic physical phenomenon. This study…
The center of mass motion of trapped ions and neutral atoms is suitable for approximation by a time-dependent driven quantum harmonic oscillator whose frequency and driving strength may be controlled with high precision. We show the time…
The presence of a cosmological constant, Lambda, in an action with higher powers of the curvature can produce rapidly oscillating metrics. We develop a perturbative approach for generating periodic solutions to the non-linear field…
Standandard Hamiltonian mechanics in its homogeneous formulation is applied to the study of discontinuities representing rapid changes of Hamiltonians. Different formulations of Hamiltonian mechanics are reviewed. An original representation…
We consider the problem of learning the dynamics of autonomous linear systems (i.e., systems that are not affected by external control inputs) from observations of multiple trajectories of those systems, with finite sample guarantees.…
We consider a quantum space with rotationally invariant noncommutative algebra of coordinates and momenta. The algebra contains tensors of noncommutativity constructed involving additional coordinates and momenta. In the rotationally…
The (non-initialized, non-deterministic) asynchronous systems (in the input-output sense) are multi-valued functions from m-dimensional signals to sets of n-dimensional signals, the concept being inspired by the modeling of the asynchronous…
A study of the non linear modes of a two degree of freedom mechanical system with bilateral elastic stop is considered. The issue related to the non-smoothness of the impact force is handled through a regularization technique. In order to…
The problem of determining the mathematical model of the dynamics of multi-dimensional control systems in the presence of noise under the condition that the correlation functions cannot be found. Known statistical dynamics of linear systems…