CAJ | 학술논문

在低维系统中,能量方程因其明晰的物理意义而得到广泛的应用,而研究高维力学系统的能量方程也同样具有理论价值和实际意义,如位移对时间的导数是速度,速度对时间的导数是加速度,这些具有明显的物理意义,而加速度的导数其物理意义就不是很清晰了,但具有理论上的意义.本文应用广义经典力学中关于广义拉格朗日函数、广义动量和广义哈密顿函数等概念,推导了高维系统的能量方程,文中举了实例具体说明新方程的应用,为力学数学系统能量方程的推广提供了一种途经.
재저유계통중,능량방정인기명석적물리의의이득도엄범적응용,이연구고유역학계통적능량방정야동양구유이론개치화실제의의,여위이대시간적도수시속도,속도대시간적도수시가속도,저사구유명현적물리의의,이가속도적도수기물리의의취불시흔청석료,단구유이론상적의의.본문응용엄의경전역학중관우엄의랍격랑일함수、엄의동량화엄의합밀돈함수등개념,추도료고유계통적능량방정,문중거료실례구체설명신방정적응용,위역학수학계통능량방정적추엄제공료일충도경.
Energy equations are widely used in low-order mechanical systems and have clear physical meanings. On the other hand, energy equations for high-order mechanical systems may lack clear meaning, but still have theoretical and practical significance. It is clear that the derivation of displacement with respect to time is velocity and the derivation of velocity with respect to time is acceleration. However, the derivation of acceleration with respect to time has no obvious physical meaning, yet it has theoretical significance. Energy equations of high-order mechanical systems were derived in this paper using the generalized Lagrange functions, generalized momentum, and the Hamilton function in generalized classical mechanics. An example was given to show the application of the new energy equations. The research in this paper provides a new way to extend the application of energy equations in mathematics and mechanical systems.