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从牛顿运动定律出发,经过逻辑推演,即可得到经典力学的全部命题,从而使经典力学成为一个优美严谨的理论体系。遗憾的是,作为经典力学的精髓——牛频第二定律,却要随坐标的选择而取不同的形式,这不能不使人怀疑它的普遍性。拉格朗日引入广义坐标和广义速度后,得到了与坐标系的选择无系的拉格朗日方程,相形之下,牛顿第二定律便为之失色。然而,它们两者却又是等价的,即从前者可以推出后者,反之也行;那末,为什么前者缺乏坐标变换不变性,而后者则不然呢?
Starting from Newton’s law of motion, all the propositions of classical mechanics can be obtained through logical deduction, so that classical mechanics becomes a beautiful and rigorous theoretical system. Unfortunately, as the essence of classical mechanics, the second law of cow frequency, takes different forms with the choice of coordinates, which can not but make people doubt its universality. Lagrange introduced generalized coordinates and generalized velocity, obtained with the choice of coordinate system of Lagrange’s equation, by contrast, Newton’s second law will be the color of it. However, both of them are equivalent, that is, the latter can be introduced from the former and vice versa. Then why does the former lack the invariance of coordinate transformation while the latter does not?