Related papers: Mathematical pendulum and its variants

Let $P$ be a collection of $n$ points moving along pseudo-algebraic trajectories in the plane. One of the hardest open problems in combinatorial and computational geometry is to obtain a nearly quadratic upper bound, or at least a subcubic…

This work deals with planar dynamical systems with and without noise. In the first part, we seek to gain a refined understanding of such systems by studying their differential-geometric transformation properties under an arbitrary smooth…

The motion of a driven planar pendulum with vertically periodically oscillating point of suspension and under the action of an additional constant torque is investigated. We study the influence of the torque strength on the transition to…

The motion of compressible, inviscid fluid under the constant pressure on a rotating sphere is studied. The hodograph equations for the corresponding Euler equation are presented. They provide us with the class of solutions of the Euler…

Small oscillations evolved a great deal from Klein to Robinson. We propose a concept of solution of differential equation based on Euler's method with infinitesimal mesh, with well-posedness based on a relation of adequality following…

We define the tangent Euler top in General Relativity through a constrained Lagrangian on the orthonormal frame bundle. The corresponding motions are studied to various degrees of approximation, the lowest of which is shown to yield the…

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…

Using the nonabilinization procedure, we find an integrable matrix version of the Euler top on $\mathfrak{so}_3$

We propose a discussion of angular momentum and its Euler equation, with the aim of giving a short outline of their history. This outline can be useful for teaching purposes too, to amend some problems that students can have in learning…

Here we present well-posedness results for first order stochastic differential inclusions, more precisely for sweeping process with a stochastic perturbation. These results are provided in combining both deterministic sweeping process…

This paper is devoted to the extension to the full $3\times3$ Euler system of the basic analytical properties of the equations governing a fluid flowing in a duct with varying section. First, we consider the Cauchy problem for a pipeline…

We use the integrable deformations method for a three-dimensional system of differential equations to obtain deformations of the T system. We analyze a deformation given by particular deformation functions. We point out that the obtained…

Newtonian dynamical systems accepting the normal shift on an arbitrary Riemannian manifold are considered. Partial differential equations forming the weak and additional normality conditions for them are reported.

We consider stochastic dynamical systems defined by differential equations with a uniform random time delay. The latter equations are shown to be equivalent to deterministic higher-order differential equations: for an $n$-th order equation…

We discuss an elementary derivation of variational symmetries and corresponding integrals of motion for the Lagrangian systems depending on acceleration. Providing several examples, we make the manuscript accessible to a wide range of…

The Euler-Bernoulli equation describing the deflection of a beam is a vital tool in structural and mechanical engineering. However, its derivation usually entails a number of intermediate steps that may confuse engineering or science…

Affine transformations in Euclidean space generates a correspondence between integrable systems on cotangent bundles to the sphere, ellipsoid and hyperboloid embedded in $R^n$. Using this correspondence and the suitable coupling constant…

A mathematical model for the poroelastic materials (PEM) with the variable volume is developed in multidimensional case. Governing equations of the model are constructed using the continuity equations, which reflect the well-known physical…

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…

This paper introduces a proof calculus for real-analytic differential-algebraic dynamic logic, enabling correct transformations of differential-algebraic equations. Applications include index reductions from differential-algebraic equations…