Related papers: On modelling bicycle power for velodromes: Part II…
We model the instantaneous power applied by a cyclist on a velodrome -- for individual pursuits and other individual time trials -- taking into account its straights, circular arcs, and connecting transition curves. The forces opposing the…
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…
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…
We combine power-meter measurements with GPS measurements to study the model that accounts for the use of power by a cyclist. The model takes into account the change in elevation and speed along with adverse effects of air, rolling and…
Power-meter measurements together with GPS measurements are used to study the model that accounts for the use of power by a cyclist. The focus is on estimating the coefficients of the air, rolling and drivetrain resistance, uncertainties of…
Power-meter measurements are used to study a model that accounts for the use of power by a cyclist. The focus is on relations between rates of change of model quantities, such as power and speed, both in the context of partial derivatives,…
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…
Experiments are reported on intermittent swimming motions. Water tunnel experiments on a nominally two-dimensional pitching foil show that the mean thrust and power scale linearly with the duty cycle, from a value of 0.2 all the way up to…
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…
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 {…
Pedestrian movements can be modeled at different degrees of detail. While flux models (Predeshensky/Milinski 1971) and cellular automata models (Schreckenberg 2002) give answers to some important questions and are fast and easy to use,…
We study stationary points of the bending energy of curves $\gamma\colon[a,b]\to\mathbb{R}^n$ subject to constraints on the arc-length and the curve's holonomy while simultaneously allowing for a variable bending stiffness along the…
This paper shows the study of interesting mechanical properties of Wilberforce pendulum. Analyzing qualitatively of the pendulum, it is able to know how the phenomenon occurs. By setting of the quantitative model, equation of the motion is…
Simple airtrack simulations, like those now possible with web-based 3D environments, can provide explorers of any age with experiential data sufficient to formulate their own models of motion. In particular, with a compressable spring, two…
We present existence, uniqueness and continuous dependence results for some kinetic equations motivated by models for the collective behavior of large groups of individuals. Models of this kind have been recently proposed to study the…
In order to describe the velocity and the anaerobic energy of two runners competing against each other for middle-distance races, we present a mathematical model relying on an optimal control problem for a system of ordinary differential…
We study general aspects of active motion with fluctuations in the speed and the direction of motion in two dimensions. We consider the case in which fluctuations in the speed are not correlated to fluctuations in the direction of motion,…
We discuss the force-velocity relations obtained in a two-state crossbridge model for molecular motors. They can be calculated analytically in two limiting cases: for a large number and for one pair of motors. The effect of the…
We investigate the dynamics of a bicycle on an uneven mountain bike track split into straight sections with small jumps (kickers) and banked corners. A basic bike-rider model is proposed and used to derive equations of motion, which capture…
For problems with multiple bodies, the current integral approach needs the use of auxiliary potential functions in order to have an individual force formula for each body. While the singularity approach, based on an extension of the…