能量守恒运动方程

IF 0.5 4区 物理与天体物理 Q4 MECHANICS
N. A. Vinokurov
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引用次数: 0

摘要

力学中的运动方程和场论中的场方程的传统推导是基于最小作用量原理和适当的拉格朗日量。对于时间无关的拉格朗日函数,坐标和速度的函数,称为能量,是常数。本文提出了一种不同的方法——推导运动方程的一般形式,以保证给出的能量作为广义坐标和相应速度的函数是恒定的。结果表明,这些是具有附加陀螺力的拉格朗日方程。这个推导明确地使用了一个重要的事实,即能量是作为构型流形的切线束上的函数给出的。拉格朗日量是由一个已知的能量函数导出的。提出了不用变分原理发展广义哈密顿方程和拉格朗日方程的方法。用这种新方法推导了一些方程。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Energy Conservation Equations of Motion

The conventional derivation of the equations of motion in mechanics and the field equations in field theory is based on the principle of least action with a proper Lagrangian. For a time-independent Lagrangian, the function of coordinates and velocities, called energy, is constant. This paper presents a different approach – derivation of the general form of the equations of motion that ensure the constancy of the energy given as a function of generalized coordinates and corresponding velocities. It is shown that these are the Lagrange equations with additional gyroscopic forces. The derivation explicitly uses the important fact that the energy is given as a function on the tangent bundle of the configuration manifold. The Lagrangian is derived from a known energy function. It is proposed to develop generalized Hamilton and Lagrange equations without using variational principles. The new technique is used to derive some equations.

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来源期刊
Doklady Physics
Doklady Physics 物理-力学
CiteScore
1.40
自引率
12.50%
发文量
12
审稿时长
4-8 weeks
期刊介绍: Doklady Physics is a journal that publishes new research in physics of great significance. Initially the journal was a forum of the Russian Academy of Science and published only best contributions from Russia in the form of short articles. Now the journal welcomes submissions from any country in the English or Russian language. Every manuscript must be recommended by Russian or foreign members of the Russian Academy of Sciences.
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