National Institute of the Republic of Serbia
ὅδε οἶκος, ὦ ἑταῖρε, μνημεῖον ἐστιν ζωῶν τῶν σοφῶν ἀνδρῶν, καὶ τῶν ἔργων αὐτῶν
Seminar for
RELATIVITY THEORY AND COSMOLOGICAL MODELS
PROGRAM
Plan rada Seminara za teoriju relativnosti i kosmološke modele za DECEMBAR 2021.
SREDA, 01.12.2021. u 11:00, Online
Hedrih (Stevanović) R. Katica, Matematički institut Srpske akademije nauka i umetnosti
ELEMENTS OF MATHEMATICAL PHENOMENOLOGY: THE THEORY OF BODY COLLISIONS IN ROLLING THROUGH GEOMETRY, KINEMATICS AND DYNAMICS OF BILLIARDS
The elements of geometry, kinematics and dynamics of rolling homogeneous balls along curvilinear lines are defined. The complete theory of the impact and collision of heavy rolling balls, through geometry, kinematics and dynamics of rolling balls, is defined. A new definition of the coefficient of restitution (collision) was introduced, starting from the hypothesis of the conservation of the sum of angular momentum of the balls in rolling, for instant rolling axes, after the collision in relation to the before collision of the bodies. The expressions for the outgoing angular velocities of the ball rolling after the collision have been derived and their rolling paths after the impact or collision have been determined and various possible anchors have been shown. The difference between the content of the term billiards used in mathematical works of many mathematicians, as well as the research that remains in the field of geometry is pointed out. These results boil down to the task of inscribing open or closed polygonal lines in some restricted areas, and anals are with tasks in optics, exploring the path of the light beam, which is reflected from mirrors at the boundaries defined by the regions. They are based on a series of Ponseleon theorems in geometry and do not reach the dynamics of real billiard systems. Our theory of ball rolling and collision is based on the examples of the abstraction of real rolling systems of heavy homogeneous billiards to a mechanical model.
Predavanja su namenjena sirokom krugu slusalaca, ukljucujuci studente redovnih i doktorskih studija. Seminar će se održavati po najavi: sredom u 11:00h, sala 301f Matematikog instituta SANU, III sprat, Knez Mihailova 36.