Related papers: The self-stabilising dynamics of bicycles
We present a new solution for fundamental problems in nonlinear dynamical systems: finding, verifying, and stabilizing cycles. The solution we propose consists of a new control method based on mixing previous states of the system (or the…
We present experimental observations and numerical simulations of a wrinkling instability that occurs at sufficiently high strain rates in the trembling regime of vesicle dynamics in steady linear flow. Spectral and statistical analysis of…
We study the stability of circular orbits of the electromagnetic two-body problem in an electromagnetic setting that includes retarded and advanced interactions. We give a method to derive the equations of tangent dynamics about circular…
Many time-trial and triathlon bicycle races take place on relatively flat, closed-circuit courses. In the absence of hills, riding-speed is limited almost solely by aerodynamic drag; consequently, winds can have a big effect on elapsed…
A huge number of technological and biological systems involves the lubricated contact between rough surfaces of soft solids in relative accelerated motion. Examples include dynamical rubber seals and the human joints. In this study we…
The classical dynamics of a particle that is driven by a rapidly oscillating potential (with frequency $\omega$) is studied. The motion is separated into a slow part and a fast part that oscillates around the slow part. The motion of the…
We study numerically some possible vortex configurations in a rotating cylinder that is tilted with respect to the rotation axis and where different numbers of vortices can be present at given rotation velocity. In a long cylinder at small…
If a system is at thermodynamic equilibrium, an observer cannot tell whether a film of it is being played forward or in reverse: any transition will occur with the same frequency in the forward as in the reverse direction. However, if…
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…
We investigate a specific reaction-diffusion system that admits a monostable pulled front propagating at constant critical speed. When a small parameter changes sign, the stable equilibrium behind the front destabilizes, due to essential…
We consider a classical problem of control of an inverted pendulum by means of a horizontal motion of its pivot point. We suppose that the control law can be non-autonomous and non-periodic w.r.t. the position of the pendulum. It is shown…
Flow instability and turbulent transition can be well explained using a new proposed theory--Energy gradient theory [1]. In this theory, the stability of a flow depends on the relative magnitude of energy gradient in streamwise direction…
Discontinuous dynamical systems with grazing solutions are discussed. The group property, continuation of solutions, continuity and smoothness of motions are thoroughly analyzed. A variational system around a grazing solution which depends…
Balancing a bicycle is typical for the balance control humans perform as a part of a whole range of behaviors (walking, running, skating, skiing, etc.). This paper presents a general model of balance control and applies it to the balancing…
Rubber friction is of major practical importance in applications such as tires, rubber seals, and footwear. This review article focuses on the theory and experimental studies of rubber friction on substrates with random roughness. We…
We develop foundational aspects of stability theory in affine logic. On the one hand, we prove appropriate affine versions of many classical results, including definability of types, existence of non-forking extensions, and other…
The Rattleback is a very popular science toy shown to students all over the world to demonstrate the non-triviality of rotational motion. When spun on a horizontal table, this boat-shaped object behaves in a peculiar way. Although the…
Previous experiments [M. J. Coleman and A. Ruina, Phys. Rev. Lett. 80, 3658 (1998)] showed that a gravity-powered toy with no control and which has no statically stable near-standing configurations can walk stably. We show here that a…
The stability of linear dynamic systems with hysteresis in feedback is considered. While the absolute stability for memoryless nonlinearities (known as Lure's problem) can be proved by the well-known circle criterion, the multivalued…
We experimentally investigate the fluidization of a granular material subject to mechanical vibrations by monitoring the angular velocity of a vane suspended in the medium and driven by an external motor. On increasing the frequency we…