相关论文: Brachistochrone on a Velodrome

The motion of a vertically positioned bicycle is considered when a horizontal control force, which maybe both internal and external in relation to the bicycle, is applied to its pedal. Tangential forces of dryfriction obeying the Euler {…

For a moving bicycle, the power can be modelled as a response to the propulsion of the centre of mass of the bicycle-cyclist system. On a velodrome, an accurate modelling of power requires a distinction between the trajectory of the wheels…

Here, I construct an elegant frictional brachistochrone for a mass point motion of a granular material with the Coulomb frictional energy dissipation that inherently includes the evolving path curvature. The simple model reveals several…

We formulate a phenomenological model to study the power applied by a cyclist on a velodrome\, -- \,for individual timetrials\, -- \,taking into account the straights, circular arcs, connecting transition curves and banking. The dissipative…

Most methods of optimal control cannot obtain accurate time-optimal protocols. The quantum brachistochrone equation is an exception, and has the potential to provide accurate time-optimal protocols for essentially any quantum control…

I discuss the influence of adding the air resistance and the kinetic friction to the classical mechanics homework-problem: finding the motion of a body sliding down a hemispherical hill. For a physically realistic ($\propto v^2$) form of…

Computing an optimal cycle in a given homology class, also referred to as the homology localization problem, is known to be an NP-hard problem in general. Furthermore, there is currently no known optimality criterion that localizes classes…

This paper studies brachistochrone trajectories. Four rules are formulated as sufficient conditions. Two rules apply for a general conservative force. Two rules apply for a central force. A central force allows wire replacement. The wire is…

We show a method to solve the problem of the brachistochrone as well as other variational problems with the help of the soap films that are formed between two suitable surfaces. We also show the interesting connection between some…

Minimum-time quantum control protocols can be obtained from the quantum brachistochrone formalism [Carlini, Hosoya, Koike, and Okudaira, Phys. Rev. Lett. 96, 06053, (2006)]. We point out that the original treatment implicitly applied the…

Influence diagrams are a decision-theoretic extension of probabilistic graphical models. In this paper we show how they can be used to solve the Brachistochrone problem. We present results of numerical experiments on this problem, compare…

A particle that moves along a smooth track in a vertical plane is influenced by two forces: gravity and normal force. The force experienced by roller coaster riders is the normal force, so a natural question to ask is: what shape of the…

Consider the motion of a Brownian particle in three dimensions, whose two spatial coordinates are standard Brownian motions with zero drift, and the remaining (unknown) spatial coordinate is a standard Brownian motion with a non-zero drift.…

We present a general framework for finding the time-optimal evolution and the optimal Hamiltonian for a quantum system with a given set of initial and final states. Our formulation is based on the variational principle and is analogous to…

The distance geometry problem asks to find a realization of a given simple edge-weighted graph in a Euclidean space of given dimension K, where the edges are realized as straight segments of lengths equal (or as close as possible) to the…

Rocking rigid bodies appear in several shapes in everyday life: As furniture like rocking chairs and rocking cradles or as toys like rocking horses or tilting dolls. The familiar rocking motion of these objects, a non-linear combination of…

The two-dimensional motion of an object on a moving rough horizontal plane is investigated. Two cases are studied: the plane having a translational acceleration, and a rotating plane. For the first case, the motions of a point particle and…

Particle sedimentation in the vicinity of a fixed horizontal vortex with time-dependent intensity can be chaotic, provided gravity is sufficient to displace the particle cloud while the vortex is off or weak. This "stretch, sediment and…

A bicycle wheel that was initially spinning freely was placed in contact with a rough surface and a digital film was made of its motion. Using Tracker software for video analysis, we obtained the velocity vectors for several points on the…

The tautochrone on a cycloid curve is usually considered without drag force. In this work, we investigate the motion of a damped cycloidal pendulum under presence of a drag force. Using the Lagrange formulation, and considering linear…