Yank和Hooke常数群
Yank and Hooke's constant group theoretically
摘要：
本文研究了（1+1）Aristotle Lie的第二中心扩张，发现第一中心扩张在（1+1）Aristotle Lie群的第二中心扩张的对偶上有四条轨道，其一般轨道由一个Hooke常数k和一个yank y表征，如果从时间演化的角度研究轨道的物理性质，它代表一个基本系统，其中内能U是在胡克力和阻尼力的共轭下的位置动量，阻尼力与速度成正比，如在粒子力学中。如果轨道的物理学是从空间演化的角度来研究的，它表示一个基本系统，其内部动量P在一种虎克力和一种阻尼力的共轭作用下，阻尼力与慢度成正比，慢度通常用于时间行波。
英文摘要：
We study the second central extension of the (1+1) Aristotle Lie.We find that the first central extension admit four orbits on the dual of second central extension of the (1+1) Aristotle Lie group.The generic orbit is characterised by a Hooke's constant k and a yank y.If the physics of the orbit is studied with respect the evolution in time,it represents an elementary system with internal energy U in a posotion-momentum under the conjugation of a Hooke's force and a damping one proportional to the velocity as in particle mechanics.If the physics of the orbit is studied with respect the evolution in space, it represents an elementary system with an internal momentum P under the conjugation of a kind of Hooke's force and a damping one proportional to a slowness, slowness usually used in time travel waves.
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