The main objective of this research is to study the properties of a billiard system in an unbounded domain with moving boundary. We consider a system consisting of an infinite rod (a straight line) and a ball (a massless point) on the plane. The rod rotates uniformly around one of its points and experiences elastic collisions with the ball. We define a mathematical model for the dynamics of such a system and write down asymptotic...

W miarę rozwoju miasta w obszar podmiejski wkraczają nie tylko nowe tereny mieszkaniowe, ale także funkcje komercyjne jak obiekty handlowe, czy sportowe. Dla osób zbliżających się do terenów zurbanizowanych przedmieście stanowi bramę wjazdową do miasta. Z tego względu powszechne jest lokalizowanie w tym obszarze różnego typu billboardów, które poprzez reklamę zapraszają do skorzystania z oferty proponowanej przez miasto. Coraz...

We consider a mechanical system consisting of an infinite rod (a straight line) and a ball (a massless point) on the plane. The rod rotates uniformly around one of its points. The ball is reflected elastically when colliding with the rod and moves freely between consecutive hits. A sliding motion along the rod is also allowed. We prove the existence and uniqueness of the motion with a given position and velocity at a certain time...

In Poland, many advertising signs addressed to motorists are located along the roadside. Advertisements do not serve any traffic related purpose and can distract drivers making them less reliable and as a consequence, reduce road safety. The existing regulations only apply to the carriageway. The research is conducted as part of the RID project. The objective of the RID project is to create a "Manual for positioning roadside advertising...