2d Stadium Billiard Trajectories Go From Boundary Points I X To J X

By keluhanqu On Sep 21, 2024 Last updated

2d Stadium Billiard Trajectories Go From Boundary Points I X To J X Download scientific diagram | 2d stadium billiard. trajectories go from boundary points i x to j x located in a segment of one quarter of the billiard wall. from publication: universality in. 2d stadium billiard. trajectories go from boundary points x i to x j located in asegment of one quarter of the billiard wall. niversality in statistical measures of classical trajectories (a)(b)(c) figure 6. 2d stadium billiard. average over trajectories. geometry parameters a b = . n = 40.

2d Stadium Billiard Trajectories Go From Boundary Points I X To J X As examples of 2d chaotic billiards, we considered the bunimovich stadium billiard and the sinai billiard. trajectories go from boundary points i x to j x located in a segment of one quarter. Figure 1. generalized bunimovich stadium. we consider billiard maps (not the ows) for two dimensional billiard tables. thus, the phase space of a billiard is the product of the boundary of the billiard table and the interval [ ˇ=2;ˇ=2] of angles of re ection. this phase space will be denoted as m. A billiard is a hamiltonian system with a 2d dimensional phase space x = (q;p) and potential v(q) = 0 for q 2q, v(q) = 1for q 2@q. remark 2.1 a billiard ﬂow has a natural poincaré section deﬁned by birkho coordinates s n, the arc length position of the nth bounce measured along the billiard boundary, and p n = jpjsin˚. First panel: 2d circular billiard. trajectories go from boundary points x i to x j located on the wall of the billiard. second panel: cardioid billiard. boundary points x i are located in one half of billiard wall. download : download full size image; download : download full size image; fig. 2. circular billiard.

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