相对论Birkhoff系统的积分不变量
Integral Invariants of Relativistic Birkhoff Systems
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摘要: 研究相对论Birkhoff系统的积分与积分不变量的构造,建立相对论Birkhoff系统的等时变分方程和非等时变分方程,由此证明:由已知系统的一个第一积分,可以构造系统的一个积分不变量.并给出了它的逆定理。Abstract: The relativistic integral invariants of Birkhoffian systems are studied. The simultaneous variant equations and non-simultaneous variant equations to the relativistic Birkhoffian systems are constructed respectively. we demonstrate a theorem, i.e. by virtue of a given first integral of the system, a integral invariant of system may be constructed, and further give it's inverse theorem.