89 research outputs found
A dynamical model of remote-control model cars
Simple experiments for which differential equations cannot be solved
analytically can be addressed using an effective model that satisfactorily
reproduces the experimental data. In this work, the one-dimensional kinematics
of a remote-control model (toy) car was studied experimentally and its
dynamical equation modelled. In the experiment, maximum power was applied to
the car, initially at rest, until it reached its terminal velocity. Digital
video recording was used to obtain the relevant kinematic variables that
enabled to plot trajectories in the phase space. A dynamical equation of motion
was proposed in which the overall frictional force was modelled as an effective
force proportional to the velocity raised to the power of a real number. Since
such an equation could not be solved analytically, a dynamical model was
developed and the system parameters were calculated by non-linear fitting.
Finally, the resulting values were substituted in the motion equation and the
numerical results thus obtained were compared with the experimental data,
corroborating the accuracy of the model.Comment: 5 pages, 9 figure
Dynamics Days Latin America and the Caribbean 2018
This book contains various works presented at the Dynamics Days Latin America and the Caribbean (DDays LAC) 2018. Since its beginnings, a key goal of the DDays LAC has been to promote cross-fertilization of ideas from different areas within nonlinear dynamics. On this occasion, the contributions range from experimental to theoretical research, including (but not limited to) chaos, control theory, synchronization, statistical physics, stochastic processes, complex systems and networks, nonlinear time-series analysis, computational methods, fluid dynamics, nonlinear waves, pattern formation, population dynamics, ecological modeling, neural dynamics, and systems biology. The interested reader will find this book to be a useful reference in identifying ground-breaking problems in Physics, Mathematics, Engineering, and Interdisciplinary Sciences, with innovative models and methods that provide insightful solutions. This book is a must-read for anyone looking for new developments of Applied Mathematics and Physics in connection with complex systems, synchronization, neural dynamics, fluid dynamics, ecological networks, and epidemics
An experiment to address conceptual difficulties in slipping and rolling problems
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 wheel, in the frame of reference of the laboratory as well as
in a relative frame of reference having as its origin the wheelâs center of
mass. The velocity of the wheelâs point of contact with the floor was also
determined obtaining then a complete picture of the kinematic state of
the wheel in both frames of reference. An empirical approach of this sort
to problems in mechanics can contribute to overcoming the considerable
difficulties they entail
Video-based analysis of the transition from slipping to rolling
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 [1-2]. Students struggle to qualitatively understand the
difference between kinetic and static frictional forcesâi.e., whereas the module of the former is known, that of
the latter can only be described in terms of an inequality while the relative velocity at the point(s) of contact is
equal to zero. In addition, students have difficulty understanding that frictional forces can act in the direction of
motionâi.e., they can accelerate object
Steady-state stabilization due to random delays in maps with self-feedback loops and in globally delayed-coupled maps
We study the stability of the fixed-point solution of an array of mutually
coupled logistic maps, focusing on the influence of the delay times,
, of the interaction between the th and th maps. Two of us
recently reported [Phys. Rev. Lett. {\bf 94}, 134102 (2005)] that if
are random enough the array synchronizes in a spatially homogeneous
steady state. Here we study this behavior by comparing the dynamics of a map of
an array of delayed-coupled maps with the dynamics of a map with
self-feedback delayed loops. If is sufficiently large, the dynamics of a
map of the array is similar to the dynamics of a map with self-feedback loops
with the same delay times. Several delayed loops stabilize the fixed point,
when the delays are not the same; however, the distribution of delays plays a
key role: if the delays are all odd a periodic orbit (and not the fixed point)
is stabilized. We present a linear stability analysis and apply some
mathematical theorems that explain the numerical results.Comment: 14 pages, 13 figures, important changes (title changed, discussion,
figures, and references added
Studentsâ conceptual difficulties in hydrodynamics
We describe a study on the conceptual difficulties faced by college students in understanding
hydrodynamics of ideal fluids. This study was based on responses obtained in hundreds of written exams
complemented with several oral interviews, which were held with first-year engineering and science
university students. Their responses allowed us to identify a series of misconceptions unreported in the
literature so far. The study findings demonstrate that the most critical difficulties arise from the studentsâ
inability to establish a link between the kinematics and dynamics of moving fluids, and from a lack of
understanding regarding how different regions of a system interact
When the Quarter Jumps into a Cup (and When It Does Not)
While Bernoulliâs equation is one of the most frequently mentioned topics in physics literature and other means of dissemination, it is also one of the least understood. Oddly enough, in the wonderful book Turning the World Inside Out, Robert Ehrlich proposes a demonstration that consists of blowing a quarter coin into a cup, incorrectly explained using Bernoulliâs equation. In the present work, we have adapted the demonstration to show situations in which the coin jumps into the cup and others in which it does not, proving that the explanation presented in Ehrlichâs book based on Bernoulliâs equation is flawed. Our demonstration is useful to tackle the common misconception, stemming from the incorrect use of this equation, that higher velocity invariably means lower pressur
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