| 微分及其在理论力学中的应用 |
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| 引用本文： | 史天治.微分及其在理论力学中的应用[J].内蒙古农业大学学报(自然科学版),2006,27(4):160-163. |
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| 作者姓名： | 史天治 |
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| 作者单位： | 淮阴师范学院物理与电子学系,淮安,223001 |
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| 摘 要： | 微分有两个含义:1.对于与时间有关的函数(称之为动态函数)f而言,微分df表示在无限小的时间dt内函数f的增加量,即df=f(t dt)-f(t);2.对于与时间无关的函数(称之为静态函数)g而言,微分dg表示g的微小部分,所有dg之和等于g。时间的微分即时间的增加量dt总是恒大于0的正实数。函数f的增加量df与时间的增加量dt之比称为函数f的增加率,而非变化率。函数f的减小量-df与时间的增加量dt之比称为函数f的减小率。变化率包括增加率与减小率两种情况。质点所受到的合外力等于它的动量的增加率。作用力与反作用力互为对偶力。保守力与势能梯度互为对偶矢量。势能定理即势能的减小量等于保守力所作的功。
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| 关 键 词： | 微分 牛顿运动定律 势能定理 增加率 减小率 变化率 理论力学 |
| 文章编号： | 1009-3575(2006)04-0160-04 |
| 收稿时间： | 2006-06-20 |
| 修稿时间： | 2006年6月20日 |
DIFFERENTIAL AND ITS APPLICATION IN THEORETICAL MECHANICS |
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| SHI Tian-zhi.DIFFERENTIAL AND ITS APPLICATION IN THEORETICAL MECHANICS[J].Journal of Inner Mongolia Agricultural University(Natural Science Edition),2006,27(4):160-163. |
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| Authors: | SHI Tian-zhi |
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| Institution: | Department of Physics and Electronics, Huaiyin Teachers College, Huaian 223001, China |
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| Abstract: | There are two meanings of differential: 1.When function f is dependent on time,which is called a dynamic function,differential df is the increment of function f in an infinitesimal time dt,i.e.df=f(t dt)-f(t).2.When function g is independent of time,which is called a static function,differential dg is an infinitesimal part of function g,the sum of all dg is equal to g.The differential of time dt is always a positive real number.The ratio of df to dt is called the rate of increment of function f.The ratio of-df to dt is called the rate of decrement of function f.Rate of increment is different from rate of change,which consists of rate of increment and rate of decrement.The resultant force acted on a particle is equal to the rate of increment of momentum of the particle.The action force and the reaction force are dual forces.The conservative force and the gradient of the potential energy are dual vectors.The potential energy theorem is that the decrement of the potential energy is equal to the work of the conservative force. |
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| Keywords: | differential Newton's Laws of Motion potential energy theorem rate of increment rate of decrement rate of change theoretical mechanics |
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