论文标题
无符号对称性的载体系统的第一积分
First integrals of holonomic systems without Noether symmetries
论文作者
论文摘要
证明了一个定理，该定理确定了表格$ i = k_ {ab}（t，q）\ dot {q}^{a} \ dot {q}^{q}^{b}+k_ {a}+k_ {a}（t，t，t，t，t，t，t，t，t，t，d dot {q）由动能或系统的Lagrangian定义的度量。它显示了如何通过反向定理将这些第一积分与测量的弱的noether对称性相关联，该对称是将给定的第一个积分作为noether积分。还可以证明，相关的noether对称性可以满足霍伊曼或形式不变性对称性的条件，因此所谓的非诺瑟式的第一个积分是衡量的弱noether积分。由于所涉及的特殊条件的复杂性，该定理的应用需要一定算法。我们通过许多解决的示例来证明该算法。我们从已发表的作品中选择示例，以证明我们的方法会产生以前与标准方法未找到的新的第一积分。
A theorem is proved which determines the first integrals of the form $I=K_{ab}(t,q)\dot{q}^{a}\dot{q}^{b}+K_{a}(t,q)\dot{q}^{a}+K(t,q)$ of autonomous holonomic systems using only the collineations of the kinetic metric which is defined by the kinetic energy or the Lagrangian of the system. It is shown how these first integrals can be associated via the inverse Noether theorem to a gauged weak Noether symmetry which admits the given first integral as a Noether integral. It is shown also that the associated Noether symmetry is possible to satisfy the conditions for a Hojman or a form-invariance symmetry therefore the so-called non-Noetherian first integrals are gauged weak Noether integrals. The application of the theorem requires a certain algorithm due to the complexity of the special conditions involved. We demonstrate this algorithm by a number of solved examples. We choose examples from published works in order to show that our approach produces new first integrals not found before with the standard methods.
