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Locomotion of bacteria by actin polymerization, and in vitro motion of spherical beads coated with a protein catalyzing polymerization, are examples of active motility. Starting from a simple model of forces locally normal to the surface of…
Circular Dyson Brownian motion describes the Brownian dynamics of particles on a circle (periodic boundary conditions), interacting through a logarithmic, long-range two-body potential. Within the log-gas picture of random matrix theory, it…
This article investigates a simple kinematical model of a disc (Disc B) rolling on the edge of a fixed disc (Disc A) to study the geometric nature of rotation. The total rotation angle $\Delta$ of Disc B after one cycle is decomposed into a…
Meteor light curves are sometimes known to display flickering: rapid, quasi-periodic variations in brightness. This effect is generally attributed to the rotational modulation of the ablation rate, which is caused by the time-varying cross…
Rotobreathers in the chain of coupled linearly elastic rotators are analyzed. Each rotator is a particle connected by a massless elastic rod with a frictionless pivot; it has two degrees of freedom, length and angle of rotation. The rods of…
We present the results of a theoretical investigation of the dynamics of a droplet walking on a vibrating fluid bath under the influence of a harmonic potential. The walking droplet's horizontal motion is described by an…
The sliding friction of a dimer moving over a periodic substrate and subjected to an external force is studied in the steady state for arbitrary temperatures within a one-dimensional model. Nonlinear phenomena that emerge include dynamic…
This article is a survey on recent contributions to an effective version of Bautin's theory about the bifurcation of periodic orbits (limit cycles). The analysis of Hopf bifurcations of higher order is possible by use of the return mapping.…
The nonlinear dynamics of an elastic filament that is forced to rotate at its base is studied by hydrodynamic simulation techniques; coupling between stretch, bend, twist elasticity and thermal fluctuations is included. The…
We discuss the equation of motion of the driven pendulum and generalize it to arbitrary driving angle. The pendulum will oscillate about a stable angle other than straight down if the drive amplitude and frequency are large enough for a…
Since Galileo's time, the pendulum has evolved into one of the most exciting physical objects in mathematical modeling due to its vast range of applications for studying various oscillatory dynamics, including bifurcations and chaos, under…
We consider the free motion of a point particle inside a circular billiard with periodically moving boundary, with the assumption that the collisions of the particle with the boundary are elastic so that the energy of the particle is not…
Stability is a key property of dynamical systems. In some cases, we want to change unstable system into stable one to achieve certain goals in engineering. Here, we present an example of a $3$ dimensional switched system that alternates…
The dynamics of a set of rods bouncing on a vertically vibrated plate is investigated using experiments, simulations, and theoretical analysis. The experiments and simulations are performed within an annulus to impose periodic boundary…
A liquid droplet is placed on a rotating helical fiber. We find that the droplet may slide down, attach or climb up the fiber. We inspect experimentally the domain of existence of these three behaviors as a function of the geometrical…
The numerical analysis for the small amplitude motion of an elastic beam with internal damping is investigated in domain with moving ends. An efficient numerical method is constructed to solve this moving boundary problem. The stability and…
We investigate the dynamics of no-slip billiards, a model in which small rotating disks may exchange linear and angular momentum at collisions with the boundary. We give new results on periodicity and boundedness of orbits which suggest…
The problem of a disc or cylinder initially rolling with slipping on a surface and subsequently transitioning to rolling without slipping is often cited in textbooks. The following experiment serves to clearly demonstrate the transition…
This paper proposes a qualitative analysis to the simple harmonic motion for students who are not mathematically well-prepared. It uses the variation in speed and acceleration to sketch the velocity-time curve. The curve appears to be…
Periodic orbit theory provides two important functions---the dynamical zeta function and the spectral determinant for the calculation of dynamical averages in a nonlinear system. Their cycle expansions converge rapidly when the system is…