arXiv · physics/0212100
Laser cooling of nuclear beams in storage rings is discussed. The main properties of nuclei with isomeric levels in the range E<50 keV are presented.
E. G. Bessonov, E. V. Tkalya. 2003-03-20. Laser Cooling of Nuclear Beams in Storage Rings. https://arxiv.org/abs/physics/0212100
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We examine two major factors that influence the optimum projection angle: aerodynamic forces and the effect of run-up. With respect to aerodynamics, we consider not only the drag but also the lift generated by spin during flight. By linearizing the equations of motion that include these forces, we derive perturbation solutions with respect to drag and lift coefficients and clarify their qualitative effects. The results show that both drag and lift reduce the optimum projection angle, with the latter exerting a stronger influence. To investigate the effect of run-up, we use an extended projection model in which the initial speed depends on the initial angle. Analysis of this model reveals that a stronger run-up increases the relative projection angle but decreases the launch angle observed from the ground. These findings provide a mechanical explanation for the release angle in shot put and the takeoff angle in long jump. The present study establishes a simple theoretical framework for clarifying the respective roles of aerodynamic and run-up effects in determining the optimum projection angles in sports.
Optimizing slender elastic structures for renewable energy applications requires non-classical continuum formulations capable of accounting for spatial micro-interactions without sacrificing analytical tractability. Here, we extend beam vibration mechanics by replacing standard spatial derivatives with the Dunkl differential operator. This modification introduces a reflection-coupled mathematical structure that accounts for spatial parity effects across the beam domain. We formulate the governing dynamic equations into a generalized eigenvalue problem and derive exact analytical expressions for modal characteristics under standard boundary conditions. The classical limit confirms exact convergence to classical Euler-Bernoulli formulations. Parametric analyses reveal that the Dunkl parameter acts as a reflection-induced modulation parameter, significantly shifting natural frequencies and altering the modal characteristics of higher modes. These results provide an analytical baseline for dynamic optimization in lightweight structural components.
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