Ostrohrads'Kyj相对论球顶动力学的微分几何机制
Differential geometric mechanisms in Ostrohrads'kyj relativistic spherical top dynamics
摘要：
从变分方程的形式理论的一些内在的工具正在工作中的应用，在三维时空中的自由相对论顶部的三阶演化方程的一个具体的例子中被证明。主要目标是引入一种组合的方法，包括同时利用对称性原理以及向量值微分形式的逆变分问题的考虑。其次，建立了自治变分问题与参数变分问题之间的转换算法。明确解决的例子表明，不存在一个整体和内在定义的拉格朗日的庞加莱不变和定义良好的唯一的变分方程的情况下在手。用泊松括号对哈密顿对应体作了简要讨论。该模型似乎提供了一个广义正则描述的准经典自旋粒子的Mathisson-Papapetrou方程在平坦的时空。
英文摘要：
Some intrinsic tools from the formal theory of variational equations are being demonstrated at work in application to one concrete example of the third-order evolution equation of free relativistic top in three-dimensional space-time. The main goal is to introduce a combined approach consisting in the simultaneous utilization of symmetry principles along with the inverse variational problem considerations in terms of vector-valued differential forms. Next, some simple algorithm of transition between the autonomous variational problem and the variational problem in parametric form is established. The example definitely solved shows no-existence of a globally and intrinsically defined Lagrangian for the Poincaré-invariant and well defined unique variational equation in the case in hand. Hamiltonian counterpart is briefly discussed in terms of Poisson bracket. The model appears to provide a generalized canonical description of the quasi-classical spinning particle governed by the Mathisson-Papapetrou equations in flat space-time.
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