质点动力学理论在平动参考系的系统性推广
Systematic generalization of particle dynamics to the translational reference frame
本文介绍了惯性力这一物理学史上长期引发争论的概念在揭示本质方面的新进展。在此基础上,系统地介绍了这一概念性的突破对改进物理教学的意义。首先,经典力学框架下的所有定理原则上都可以推广到任何的平动参考系,前提是将原表述中质点受力项的物理意义从统计全部受力替换为统计相对的受力。其次,在分析力学中,由于在一般情况下,与势能相对应的保守力通常是作用在质点上的力的一部分,因此只需确保将参考原点选在与势能相对应的保守力的矢量和始终为零的位置即可。然而,在一般平动参考系的情况下,必须在拉格朗日量和哈密顿量的表达式中加入一个因作用在参考物上的力而导致的势能修正项。最后,质点动力学的对称新方程同样可以自然推广到质点系。在平动参考系中建立推广的质心运动定理和推广的定轴转动定理。最后,为体现实用上的改进优势, 讨论了多体动力学。原则上,在传统方案中通过引入质心参考系来应用牛顿第二定律,看似严格,不过带来了步骤上的迂回。相比之下,通过应用牛顿动力学的对称新方程,行星摄动方程的推导一步到位直截了当。更重要的是,多体系统的质心参考系严格地说仍然只是对惯性系的更高阶近似, 因此,通过考虑非引力相互作用,乃至天体系统外的其他受力,只有对称新方程才可以真正严格地得到行星摄动方程在经典力学框架下的所有可能修正。
his paper presents a new development in revealing the nature of the inertial force, a concept that has long stimulated discussion in the history of physics. On this basis, its implications are systematically introduced for the improvement of physics teaching. Firstly, all the theorems in the framework of classical mechanics can be form-invariant generalized to any translational frame of reference, provided that the physical meaning of the force term of the particle in the original formulation is replaced from the total forces to the forces being relatively accounted for. Secondly, in analytical mechanics, since in general the conservative force corresponding to the potential energy is typically a part of the forces acting on the particle, it is enough to ensure that the reference origin is chosen at a position where the vector sum of the conservative forces corresponding to the potential energy is always zero. However, in the case of a general translational reference frame, a correction term for the potential energy due to the forces acting on the reference object must be included in the expression of the Lagrangian and Hamiltonian quantities. Thirdly, the symmetric new equation is applied to the system of particles. The generalized center-of-mass motion theorem and the generalized fixed-axis rotation theorem in the translational reference frame are developed. Finally, for instance, the multi-body dynamics is discussed. In principle, the detour that is introduced by the center-of-mass reference frame can be directly omitted and crossed. To illustrate this, the planetary perturbation equation is demonstrated to be derived in a single step by applying the symmetric new equation of Newtonian dynamics. Besides, the introduction of the symmetric new equation has led to further improvements and refinements in the planetary perturbation equation.
陈驰一
力学物理学
惯性力参考物质点动力学平动参考系适度相对性原理
Inertial forceReference objectParticle dynamicsTranslational reference frameModerate principle of relativity
陈驰一.质点动力学理论在平动参考系的系统性推广[EB/OL].(2024-07-18)[2025-08-23].https://chinaxiv.org/abs/202407.00221.点此复制
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