跳跃振荡器
Jumping oscillator
摘要：
研究表明，一个勒让德变换沿超曲面退化的拉格朗日系统的行为是一种奇怪的方式，从时间到时间的跳跃没有任何“可见的原因”。在这样一个跳跃中，系统的坐标和动量都在瞬间改变。这一现象的数学描述是基于一位作者提出的碰撞、折射和反射理论，以及对哈密顿量向量场（被理解为相对场）可以与任何拉格朗日量（退化或非退化）相关联的观察。必要的元素，这样的系统的一般理论的报告和一个后相对论振荡器显示这样的行为给出了详细的描述。
英文摘要：
It is shown that a lagrangian system whose Legendre transformation degenerates along a hypersurface behaves in a strange manner by jumping from time to time without any ''visible cause''. In such a jump the system changes instantaneously its coordinates as well as its momenta. The mathematical dscription of the phenomenon is based on the theory of impact, refraction and reflection developed by one of the authors and the observation that a hamiltonian vector field, understood as a relative one, can be associated with any lagrangian, degenerated or not. Necessary elements of the general theory of such systems are reported and a detailed description of a post-relativistic oscillator showing such a behaviour is given.
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