Has the Problem of the Motion of a Heavy Symmetric Top been Solved in Quadratures?

IF 1.2 3区物理与天体物理 Q3 PHYSICS, MULTIDISCIPLINARY

Foundations of Physics Pub Date : 2024-06-20 DOI:10.1007/s10701-024-00771-9

Alexei A. Deriglazov

引用次数: 0

Abstract

We have revised the problem of the motion of a heavy symmetric top. When formulating equations of the Lagrange top with the diagonal inertia tensor, the potential energy has more complicated form as compared with that assumed in the literature on dynamics of a rotating body. This implies the corresponding improvements in equations of motion. Using the Liouville’s theorem, we solve the improved equations in quadratures and present the explicit expressions for the resulting elliptic integrals.

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对称重顶的运动问题是否已用四则运算解决？

我们修改了重对称顶的运动问题。在用对角惯性张量建立拉格朗日陀螺方程时，势能的形式与旋转体动力学文献中假设的势能形式相比更为复杂。这意味着运动方程的相应改进。利用柳维尔定理，我们对改进后的方程进行了二次求解，并给出了所得椭圆积分的明确表达式。

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来源期刊

Foundations of Physics 物理-物理：综合

CiteScore

2.70

自引率

6.70%

发文量

104

审稿时长

6-12 weeks

期刊介绍： The conceptual foundations of physics have been under constant revision from the outset, and remain so today. Discussion of foundational issues has always been a major source of progress in science, on a par with empirical knowledge and mathematics. Examples include the debates on the nature of space and time involving Newton and later Einstein; on the nature of heat and of energy; on irreversibility and probability due to Boltzmann; on the nature of matter and observation measurement during the early days of quantum theory; on the meaning of renormalisation, and many others. Today, insightful reflection on the conceptual structure utilised in our efforts to understand the physical world is of particular value, given the serious unsolved problems that are likely to demand, once again, modifications of the grammar of our scientific description of the physical world. The quantum properties of gravity, the nature of measurement in quantum mechanics, the primary source of irreversibility, the role of information in physics – all these are examples of questions about which science is still confused and whose solution may well demand more than skilled mathematics and new experiments. Foundations of Physics is a privileged forum for discussing such foundational issues, open to physicists, cosmologists, philosophers and mathematicians. It is devoted to the conceptual bases of the fundamental theories of physics and cosmology, to their logical, methodological, and philosophical premises. The journal welcomes papers on issues such as the foundations of special and general relativity, quantum theory, classical and quantum field theory, quantum gravity, unified theories, thermodynamics, statistical mechanics, cosmology, and similar.