Related papers: Linearisation of Simple Pendulum
Rowmotion is a simple cyclic action on the distributive lattice of order ideals of a poset: it sends the order ideal x to the order ideal generated by the minimal elements not in x. It can also be computed in "slow motion" as a sequence of…
The measurement of a quantum system becomes itself a quantum-mechanical process once the apparatus is internalized. That shift of perspective may result in different physical predictions for a variety of reasons. We present a model…
We present an experimental setup to demonstrate normal modes and symmetry breaking in a two-dimensional pendulum. In our experiment we have used two modes of a single oscillator to demonstrate normal modes, as opposed to two single…
The constants of motion of the following systems are deduced: a relativistic particle with linear dissipation, a no-relativistic particle with a time explicitly depending force, a no-relativistic particle with a constant force and time…
The equation of motion announced in the title was already deduced for the cases the inner metric being flat and the shell being negligibly small (test matter), using surface layers and geodesic trajectories resp. Here we derive the general…
We show asymptotic, exponential stability of the equilibrium configuration, $\smallL$, of a hollow physical pendulum with its inner part entirely filled with a viscous liquid, corresponding to the center of mass being in the lowest…
We provide new existence and uniqueness results for the discrete-time Hamilton (DTH) equations of a symplectic-energy-momentum (SEM) integrator. In particular, we identify points in extended-phase space where the DTH equations of SEM…
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,…
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…
In this paper we show that there are applications that transform the movement of a pendulum into movements in $\mathbb{R}^3$. This can be done using Euler top system of differential equations. On the constant level surfaces, Euler top…
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…
An approximate solution is presented for simple harmonic motion in the presence of damping by a force which is a general power-law function of the velocity. The approximation is shown to be quite robust, allowing for a simple way to…
In the present paper, the nonlinear differential equation of pendulum is investigated to find an exact closed form solution, satisfying governing equation as well as initial conditions. The new concepts used in the suggested method are…
An inverted planar pendulum with horizontally moving pivot point is considered. It is assumed that the law of motion of the pivot point is given and the pendulum is moving in the presence of dry friction. Sufficient conditions for the…
We study the motion of the coupled system, $\mathscr S$, constituted by a physical pendulum, $\mathscr B$, with an interior cavity entirely filled with a viscous, compressible fluid, $\mathscr F$. The presence of the fluid may strongly…
The motion of a charged particle moving on a flat surface is studied through the constants of motion associated to the system, given the magnetic gauge. The usual Landau' solution and the non separable solution for the Landau's gauge are…
The swinging spring, or elastic pendulum, has a 2:1:1 resonance arising at cubic order in its approximate Lagrangian. The corresponding modulation equations are the well-known three-wave equations that also apply, for example, in…
We investigate the motion of a massive particle constrained to move along a path consisting of two line segments on a vertical plane under an arbitrary conservative force. By fixing the starting and end points of the track and varying the…
We present the basic formulation of Hamilton dynamics in complex phase space. We extend the Hamilton's function by including the imaginary part and find out the corresponding Hamilton's canonical equation of motion. Example of simple…
Simplicial homology manifolds are proposed as an interesting class of geometric objects, more general than topological manifolds but still quite tractable, in which questions about the microstructure of space-time can be naturally…