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Dear Friends ! Without your comments to current topics we will not be able to proceed our quest in order to bring together mathematics and engineering ! Please do not hesitate to comment, ask questions, request proceedings of the currently published articles and software !
In this picture you can see how flow of some fluid in a
cavity turns around (Reynolds number of the flud is 10000):
In fact, this is a computed simulation of water
flow in some cavity, where the arrows show the directions of flow
particles. This simulation is based on the so-called
Navier-Stockes-Equations, which describe mathematically any fluid
flow, and are used, for example, in order to predict weather
or design airplanes.
Allthough Navier-Stockes equations, which can be helpful to describe
the behaviour of any fluid on the Earth, are obtained in a
pure mathematical way (not through experiments), they seem to be true as shown by
experiments and they are ... mysterious ! Because nobody knows, wheather these
mathematically obtained equations have a mathematical solution. This
problem is one of the famous ... Read more » |
Bézier curves were inveted in 1962 by the french engineer Pierre Bézier, who used them to design automobile bodies. Bézier curves are an important tool in comuter graphics and image manipulation programs such as Adobe Illustrator, Adobe Photoshop, and GIMP. Bézier curves are also used in animation as a tool to control motion in applications such as Adobe Flash, Adobe After Effects, Microsoft Expression Blend, Blender, and Autodesk 3ds max. Let's experiment with Bézier curves: http://optimizationeng.ucoz.com/freeform1/Freeform.html |
Laser Beam Welding in automitve or aeronautics manufacturing using industrial robots with 6 arms is a modern welding
process of a great economics importance that continues to expand into
modern industries and new applications because of its many advantages
like deep weld penetration or minimizing heat inputs. But one of the key advantages of laser welidng - the possibility to performe remote welding from the distance about 1 m. In this way the
total amount of robot motion and energy expenses can be reduced. However, on the other hand, any robot motion leads to
natural mechanical vibrations which cause fatal inexactness of welding, especially, in the case of remote welding (from the distance about 1m). These considerations lead to the question:
... Read more » |
Design of mechanisms in usual 3-dimensional space may require the knowledge about exact trajectories ot its parts during the mechanism motion. In order to imagine or compute them one cann't avoid the consideration of additional dimensions. For the purposes of brevity we shall consider the 2-dimensional example - the plane circle (given by equation y2+x2=2) moving along a parabola ( y=x2):
What curve will be described by extemal points of the moving plane circle ? This curve (called envelope) can be calculated by introducing additional dimension - time and corresponding varable t. As shown by computations demonstrated in < ... Read more » |
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