Abstract
During the 21st century and the incredible development of the information sector the way image-based data is processed has also changed. Nowadays 3D scanning does not cause any problems either: new tools and methods have made it possible for geometries to be easily read, modelled and visualised. However, applying these techniques is not always possible. Even today, the information collected by rovers and satellites in aerospace research is still mostly transmitted in the form of data sets and photos.
Understanding the morphology of the surface of the Mars can be made easier by observing the geometry of the pebbles found there. International research has been examining the possibilities of the formation of Martian pebbles and their form-evolution. While the number of static equilibrium points would be one of the most important pieces of information related to the subject, according to current scientific knowledge, using nothing but projections (such as the images made by the Curiosity Mars Rover) it is impossible to determine which equilibrium class the observed pebble belongs to.
In my study I am going to approach the problem from a different angle: are there any special convex bodies that we can sort into stability classes just by knowing their projections – and if such bodies do exist, then how would it be possible to construct them in a simple way?
On the one hand this study can bring us closer to the understanding of the original problem, and on the other hand it will also present how the stability classes – which are currently used to describe natural forms – can be simply illustrated. To exemplify this, I will use an extremely important subset of the stability classes, the one that contains those classes where the equation S, U < 5 is true – meaning that the number of both the stable and unstable equilibrium points is less than five.
The scientific significance of the chosen subset lies in the fact that more than 98 percent of the coastal pebbles belong to one of these classes. By focusing on these examples the present study bears a stronger connection to current trends in research. Though it does not attempt to present and decode the geometries of natural pebbles, it will visualise the stability classes in question by using bodies which can be easily described mathematically.
The presented results and figures have been created by a self-written Wolfram Mathematica script.
