变维分形形式的牛顿第二定律及万有引力定律和库仑定律

Newton's second Law, the law of Gravity and the law of Coulomb with the form of variable dimension fractal

在理论上导出常维分形形式的牛顿第二定律及万有引力定律和库仑定律的基础上,对自由落体运动(中心对中心运动),从理论上严格导出原有的牛顿第二定律F=ma、并针对一个小球沿长斜面滚下的实例近似导出原有的万有引力定律和库仑定律.在此基础上,针对小球沿长斜面滚下的实例进一步导出更精确的变维分形结果:改进的牛顿第二定律F=am1+ε,ε=8.779×10-8x;改进的万有引力定律F=-GMm/r2-δ,δ=1.206×10-12x;改进的库仑定律f=kq1q2/r2-δ.δ=1.206×10-12x;其中x为小球滚下的水平距离(对于初始的静止状态,x=0).另外,对于文中实例,如果要求计算结果具有5位有效数字,则狭义相对论的结果与原有的第二定律结果一样.

On deriving Newton's second law . the law of gravity and the law of Coulomb with the form of constant dimension fractal theoretically, for free fall movement (center to center movement), the original Newton's second law F=ma, is derived strictly and theoretically, for an example (a small ball moves down along a long incline), the original law of gravity and the original law of Coulomb are derived approximately and theoretically. Based on these, for the example that a small ball moves down along a long incline the more accurate results with the form of variable dimension fractal are as follows, improved Newton's second law: F= ma1+ε, ε = 8. 779 ×r 10-8 x; improved law of gravity. F = -GMm/r2-δ,δ= 1.206 × -12 x ; improved law of Coulomb :f=kq1q2/r2-δ,δ= 1. 206 × 10 12x; where x equals the horizontal distance of the small ball movement (for the beginning static state,x=0 ). In addition, to the example given in this paper, for the result of five significant digits, the special relativity will give the same result as given by the original Newton's second law.