PLAN RADA SEMINARA ZA FEBRUAR 2022. GODINE

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Utorak, 22.02.2022. u 14:15, Online
Hedrih (Stevanović) R. Katica, Mathematical Institute of Serbian Academy of Sciences and Arts, Belgrade, Serbia; Faculty of Mechanical Engineering at University of Niš, Serbia
ROLLING PENDULUMS ALONG CURVILINEAR TRACES AND SURFACES: COLLISION THEORY AND DYNAMICS OF VIBRO-IMPACT SYSTEMS: AN OVERVIEW
An overview of the new derived nonlinear differential equations and phase trajectory equations of the body's rolling along curvilinear stationary and rotating curvilinear line - trajectories, as examples of rolling pendulums with one degree of freedom is done. An appropriate system of coupled nonlinear differential equations for a homogeneous heavy ball rolling on an arbitrary surface with all elements of geometry, kinematics and rolling dynamics was performed. A generalization is given for the example of rolling a ball along the coordinate surfaces of functional nonlinear coordinate systems of curvilinear orthogonal coordinates, using the base vectors of the tangent space of the vector of the position of the contact point of the ball in rolling with the coordinate surface at which it rolls.
Based on Petrovic's theory Elements of Mathematical Phenomenology and Phenomenological Mapping, the theory of collisions between rolling bodies through geometry, kinematics and dynamics of impact and collision of balls in rolling is formulated, and examples of the dynamics of vibro-impact systems containing rolling balls are given.

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