User:Yuezhe Li

Denote $$q=\frac{2\, {\left(\frac{7290000}{{\left(a + \frac{1}{10}\right)}^2} + {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2 + \frac{729}{2500}\right)}^3}{27} - \frac{\left(\frac{7290000}{{\left(a + \frac{1}{10}\right)}^2} + {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2 + \frac{729}{2500}\right)\, \left(\frac{2125764}{{\left(a + \frac{1}{10}\right)}^2} + \frac{729\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{2500} + \frac{7290000\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{{\left(a + \frac{1}{10}\right)}^2}\right)}{3} + \frac{2125764\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{{\left(a + \frac{1}{10}\right)}^2} - \frac{2500\, \left(\frac{4345080004734585\, r^8}{68719476736} + \frac{384160000\, a^4\, {\mathrm{ara}}^4}{{\left(\frac{181\, {\mathrm{ara}}^2}{81} + \frac{4525}{324}\right)}^2} + 1\right)}{a^2\, \left(\frac{21778071482940061661655974875633165533184\, r^8}{53817251171012308427455331739009} + \frac{10000\, a^4\, {\mathrm{ara}}^4}{{\left(\frac{181\, {\mathrm{ara}}^2}{81} + \frac{4525}{324}\right)}^2} + 1\right)}$$

$$p=\frac{2125764}{{\left(a + \frac{1}{10}\right)}^2} + \frac{729\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{2500} - \frac{{\left(\frac{7290000}{{\left(a + \frac{1}{10}\right)}^2} + {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2 + \frac{729}{2500}\right)}^2}{3} + \frac{7290000\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{{\left(a + \frac{1}{10}\right)}^2} $$

$$\Delta=\frac{{\left(\frac{2\, {\left(\frac{7290000}{{\left(a + \frac{1}{10}\right)}^2} + {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2 + \frac{729}{2500}\right)}^3}{27} - \frac{\left(\frac{7290000}{{\left(a + \frac{1}{10}\right)}^2} + {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2 + \frac{729}{2500}\right)\, \left(\frac{2125764}{{\left(a + \frac{1}{10}\right)}^2} + \frac{729\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{2500} + \frac{7290000\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{{\left(a + \frac{1}{10}\right)}^2}\right)}{3} + \frac{2125764\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{{\left(a + \frac{1}{10}\right)}^2} - \frac{2500\, \left(\frac{4345080004734585\, r^8}{68719476736} + \frac{384160000\, a^4\, {\mathrm{ara}}^4}{{\left(\frac{181\, {\mathrm{ara}}^2}{81} + \frac{4525}{324}\right)}^2} + 1\right)}{a^2\, \left(\frac{21778071482940061661655974875633165533184\, r^8}{53817251171012308427455331739009} + \frac{10000\, a^4\, {\mathrm{ara}}^4}{{\left(\frac{181\, {\mathrm{ara}}^2}{81} + \frac{4525}{324}\right)}^2} + 1\right)}\right)}^2}{4} + \frac{{\left(\frac{2125764}{{\left(a + \frac{1}{10}\right)}^2} + \frac{729\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{2500} - \frac{{\left(\frac{7290000}{{\left(a + \frac{1}{10}\right)}^2} + {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2 + \frac{729}{2500}\right)}^2}{3} + \frac{7290000\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{{\left(a + \frac{1}{10}\right)}^2}\right)}^3}{27} $$ 总存在震动周期. 但是当 $$q<0$$ 时存在震动周期为负数或者周期==0，从而在实际过程中出现不震动现象（左行解不能向右延拓）.

if $$q>0$$ $$\Delta \geq 0 \Longrightarrow $$ 1个振动中心 此时有周期==$$\frac{2\, \pi}{{\left(\sqrt{\frac{{\left(\frac{2\, {\left(\frac{7290000}{{\left(a + \frac{1}{10}\right)}^2} + {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2 + \frac{729}{2500}\right)}^3}{27} - \frac{\left(\frac{7290000}{{\left(a + \frac{1}{10}\right)}^2} + {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2 + \frac{729}{2500}\right)\, \left(\frac{2125764}{{\left(a + \frac{1}{10}\right)}^2} + \frac{729\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{2500} + \frac{7290000\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{{\left(a + \frac{1}{10}\right)}^2}\right)}{3} + \frac{2125764\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{{\left(a + \frac{1}{10}\right)}^2} - \frac{2500\, \left(\frac{4345080004734585\, r^8}{68719476736} + \frac{384160000\, a^4\, {\mathrm{ara}}^4}{{\left(\frac{181\, {\mathrm{ara}}^2}{81} + \frac{4525}{324}\right)}^2} + 1\right)}{a^2\, \left(\frac{21778071482940061661655974875633165533184\, r^8}{53817251171012308427455331739009} + \frac{10000\, a^4\, {\mathrm{ara}}^4}{{\left(\frac{181\, {\mathrm{ara}}^2}{81} + \frac{4525}{324}\right)}^2} + 1\right)}\right)}^2}{4} + \frac{{\left(\frac{2125764}{{\left(a + \frac{1}{10}\right)}^2} + \frac{729\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{2500} - \frac{{\left(\frac{7290000}{{\left(a + \frac{1}{10}\right)}^2} + {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2 + \frac{729}{2500}\right)}^2}{3} + \frac{7290000\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{{\left(a + \frac{1}{10}\right)}^2}\right)}^3}{27}} - \frac{{\left(\frac{7290000}{{\left(a + \frac{1}{10}\right)}^2} + {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2 + \frac{729}{2500}\right)}^3}{27} + \frac{\left(\frac{7290000}{{\left(a + \frac{1}{10}\right)}^2} + {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2 + \frac{729}{2500}\right)\, \left(\frac{2125764}{{\left(a + \frac{1}{10}\right)}^2} + \frac{729\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{2500} + \frac{7290000\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{{\left(a + \frac{1}{10}\right)}^2}\right)}{6} - \frac{1062882\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{{\left(a + \frac{1}{10}\right)}^2} + \frac{1250\, \left(\frac{4345080004734585\, r^8}{68719476736} + \frac{384160000\, a^4\, {\mathrm{ara}}^4}{{\left(\frac{181\, {\mathrm{ara}}^2}{81} + \frac{4525}{324}\right)}^2} + 1\right)}{a^2\, \left(\frac{21778071482940061661655974875633165533184\, r^8}{53817251171012308427455331739009} + \frac{10000\, a^4\, {\mathrm{ara}}^4}{{\left(\frac{181\, {\mathrm{ara}}^2}{81} + \frac{4525}{324}\right)}^2} + 1\right)}\right)}^{\frac{1}{3}} + {\left(\frac{\left(\frac{7290000}{{\left(a + \frac{1}{10}\right)}^2} + {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2 + \frac{729}{2500}\right)\, \left(\frac{2125764}{{\left(a + \frac{1}{10}\right)}^2} + \frac{729\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{2500} + \frac{7290000\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{{\left(a + \frac{1}{10}\right)}^2}\right)}{6} - \frac{{\left(\frac{7290000}{{\left(a + \frac{1}{10}\right)}^2} + {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2 + \frac{729}{2500}\right)}^3}{27} - \sqrt{\frac{{\left(\frac{2\, {\left(\frac{7290000}{{\left(a + \frac{1}{10}\right)}^2} + {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2 + \frac{729}{2500}\right)}^3}{27} - \frac{\left(\frac{7290000}{{\left(a + \frac{1}{10}\right)}^2} + {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2 + \frac{729}{2500}\right)\, \left(\frac{2125764}{{\left(a + \frac{1}{10}\right)}^2} + \frac{729\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{2500} + \frac{7290000\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{{\left(a + \frac{1}{10}\right)}^2}\right)}{3} + \frac{2125764\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{{\left(a + \frac{1}{10}\right)}^2} - \frac{2500\, \left(\frac{4345080004734585\, r^8}{68719476736} + \frac{384160000\, a^4\, {\mathrm{ara}}^4}{{\left(\frac{181\, {\mathrm{ara}}^2}{81} + \frac{4525}{324}\right)}^2} + 1\right)}{a^2\, \left(\frac{21778071482940061661655974875633165533184\, r^8}{53817251171012308427455331739009} + \frac{10000\, a^4\, {\mathrm{ara}}^4}{{\left(\frac{181\, {\mathrm{ara}}^2}{81} + \frac{4525}{324}\right)}^2} + 1\right)}\right)}^2}{4} + \frac{{\left(\frac{2125764}{{\left(a + \frac{1}{10}\right)}^2} + \frac{729\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{2500} - \frac{{\left(\frac{7290000}{{\left(a + \frac{1}{10}\right)}^2} + {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2 + \frac{729}{2500}\right)}^2}{3} + \frac{7290000\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{{\left(a + \frac{1}{10}\right)}^2}\right)}^3}{27}} - \frac{1062882\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{{\left(a + \frac{1}{10}\right)}^2} + \frac{1250\, \left(\frac{4345080004734585\, r^8}{68719476736} + \frac{384160000\, a^4\, {\mathrm{ara}}^4}{{\left(\frac{181\, {\mathrm{ara}}^2}{81} + \frac{4525}{324}\right)}^2} + 1\right)}{a^2\, \left(\frac{21778071482940061661655974875633165533184\, r^8}{53817251171012308427455331739009} + \frac{10000\, a^4\, {\mathrm{ara}}^4}{{\left(\frac{181\, {\mathrm{ara}}^2}{81} + \frac{4525}{324}\right)}^2} + 1\right)}\right)}^{\frac{1}{3}}} $$ 周期对于ara的导数==$$-\frac{2\, \pi\, \left(\frac{\frac{\left(\frac{2500\, \left(\frac{1536640000\, a^4\, {\mathrm{ara}}^3}{{\left(\frac{181\, {\mathrm{ara}}^2}{81} + \frac{4525}{324}\right)}^2} - \frac{278131840000\, a^4\, {\mathrm{ara}}^5}{81\, {\left(\frac{181\, {\mathrm{ara}}^2}{81} + \frac{4525}{324}\right)}^3}\right)}{a^2\, \left(\frac{21778071482940061661655974875633165533184\, r^8}{53817251171012308427455331739009} + \frac{10000\, a^4\, {\mathrm{ara}}^4}{{\left(\frac{181\, {\mathrm{ara}}^2}{81} + \frac{4525}{324}\right)}^2} + 1\right)} - \frac{2500\, \left(\frac{40000\, a^4\, {\mathrm{ara}}^3}{{\left(\frac{181\, {\mathrm{ara}}^2}{81} + \frac{4525}{324}\right)}^2} - \frac{7240000\, a^4\, {\mathrm{ara}}^5}{81\, {\left(\frac{181\, {\mathrm{ara}}^2}{81} + \frac{4525}{324}\right)}^3}\right)\, \left(\frac{4345080004734585\, r^8}{68719476736} + \frac{384160000\, a^4\, {\mathrm{ara}}^4}{{\left(\frac{181\, {\mathrm{ara}}^2}{81} + \frac{4525}{324}\right)}^2} + 1\right)}{a^2\, {\left(\frac{21778071482940061661655974875633165533184\, r^8}{53817251171012308427455331739009} + \frac{10000\, a^4\, {\mathrm{ara}}^4}{{\left(\frac{181\, {\mathrm{ara}}^2}{81} + \frac{4525}{324}\right)}^2} + 1\right)}^2}\right)\, \left(\frac{2\, {\left(\frac{7290000}{{\left(a + \frac{1}{10}\right)}^2} + {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2 + \frac{729}{2500}\right)}^3}{27} - \frac{\left(\frac{7290000}{{\left(a + \frac{1}{10}\right)}^2} + {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2 + \frac{729}{2500}\right)\, \left(\frac{2125764}{{\left(a + \frac{1}{10}\right)}^2} + \frac{729\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{2500} + \frac{7290000\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{{\left(a + \frac{1}{10}\right)}^2}\right)}{3} + \frac{2125764\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{{\left(a + \frac{1}{10}\right)}^2} - \frac{2500\, \left(\frac{4345080004734585\, r^8}{68719476736} + \frac{384160000\, a^4\, {\mathrm{ara}}^4}{{\left(\frac{181\, {\mathrm{ara}}^2}{81} + \frac{4525}{324}\right)}^2} + 1\right)}{a^2\, \left(\frac{21778071482940061661655974875633165533184\, r^8}{53817251171012308427455331739009} + \frac{10000\, a^4\, {\mathrm{ara}}^4}{{\left(\frac{181\, {\mathrm{ara}}^2}{81} + \frac{4525}{324}\right)}^2} + 1\right)}\right)}{4\, \sqrt{\frac{{\left(\frac{2\, {\left(\frac{7290000}{{\left(a + \frac{1}{10}\right)}^2} + {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2 + \frac{729}{2500}\right)}^3}{27} - \frac{\left(\frac{7290000}{{\left(a + \frac{1}{10}\right)}^2} + {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2 + \frac{729}{2500}\right)\, \left(\frac{2125764}{{\left(a + \frac{1}{10}\right)}^2} + \frac{729\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{2500} + \frac{7290000\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{{\left(a + \frac{1}{10}\right)}^2}\right)}{3} + \frac{2125764\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{{\left(a + \frac{1}{10}\right)}^2} - \frac{2500\, \left(\frac{4345080004734585\, r^8}{68719476736} + \frac{384160000\, a^4\, {\mathrm{ara}}^4}{{\left(\frac{181\, {\mathrm{ara}}^2}{81} + \frac{4525}{324}\right)}^2} + 1\right)}{a^2\, \left(\frac{21778071482940061661655974875633165533184\, r^8}{53817251171012308427455331739009} + \frac{10000\, a^4\, {\mathrm{ara}}^4}{{\left(\frac{181\, {\mathrm{ara}}^2}{81} + \frac{4525}{324}\right)}^2} + 1\right)}\right)}^2}{4} + \frac{{\left(\frac{2125764}{{\left(a + \frac{1}{10}\right)}^2} + \frac{729\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{2500} - \frac{{\left(\frac{7290000}{{\left(a + \frac{1}{10}\right)}^2} + {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2 + \frac{729}{2500}\right)}^2}{3} + \frac{7290000\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{{\left(a + \frac{1}{10}\right)}^2}\right)}^3}{27}}} + \frac{1250\, \left(\frac{1536640000\, a^4\, {\mathrm{ara}}^3}{{\left(\frac{181\, {\mathrm{ara}}^2}{81} + \frac{4525}{324}\right)}^2} - \frac{278131840000\, a^4\, {\mathrm{ara}}^5}{81\, {\left(\frac{181\, {\mathrm{ara}}^2}{81} + \frac{4525}{324}\right)}^3}\right)}{a^2\, \left(\frac{21778071482940061661655974875633165533184\, r^8}{53817251171012308427455331739009} + \frac{10000\, a^4\, {\mathrm{ara}}^4}{{\left(\frac{181\, {\mathrm{ara}}^2}{81} + \frac{4525}{324}\right)}^2} + 1\right)} - \frac{1250\, \left(\frac{40000\, a^4\, {\mathrm{ara}}^3}{{\left(\frac{181\, {\mathrm{ara}}^2}{81} + \frac{4525}{324}\right)}^2} - \frac{7240000\, a^4\, {\mathrm{ara}}^5}{81\, {\left(\frac{181\, {\mathrm{ara}}^2}{81} + \frac{4525}{324}\right)}^3}\right)\, \left(\frac{4345080004734585\, r^8}{68719476736} + \frac{384160000\, a^4\, {\mathrm{ara}}^4}{{\left(\frac{181\, {\mathrm{ara}}^2}{81} + \frac{4525}{324}\right)}^2} + 1\right)}{a^2\, {\left(\frac{21778071482940061661655974875633165533184\, r^8}{53817251171012308427455331739009} + \frac{10000\, a^4\, {\mathrm{ara}}^4}{{\left(\frac{181\, {\mathrm{ara}}^2}{81} + \frac{4525}{324}\right)}^2} + 1\right)}^2}}{3\, {\left(\frac{\left(\frac{7290000}{{\left(a + \frac{1}{10}\right)}^2} + {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2 + \frac{729}{2500}\right)\, \left(\frac{2125764}{{\left(a + \frac{1}{10}\right)}^2} + \frac{729\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{2500} + \frac{7290000\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{{\left(a + \frac{1}{10}\right)}^2}\right)}{6} - \frac{{\left(\frac{7290000}{{\left(a + \frac{1}{10}\right)}^2} + {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2 + \frac{729}{2500}\right)}^3}{27} - \sqrt{\frac{{\left(\frac{2\, {\left(\frac{7290000}{{\left(a + \frac{1}{10}\right)}^2} + {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2 + \frac{729}{2500}\right)}^3}{27} - \frac{\left(\frac{7290000}{{\left(a + \frac{1}{10}\right)}^2} + {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2 + \frac{729}{2500}\right)\, \left(\frac{2125764}{{\left(a + \frac{1}{10}\right)}^2} + \frac{729\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{2500} + \frac{7290000\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{{\left(a + \frac{1}{10}\right)}^2}\right)}{3} + \frac{2125764\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{{\left(a + \frac{1}{10}\right)}^2} - \frac{2500\, \left(\frac{4345080004734585\, r^8}{68719476736} + \frac{384160000\, a^4\, {\mathrm{ara}}^4}{{\left(\frac{181\, {\mathrm{ara}}^2}{81} + \frac{4525}{324}\right)}^2} + 1\right)}{a^2\, \left(\frac{21778071482940061661655974875633165533184\, r^8}{53817251171012308427455331739009} + \frac{10000\, a^4\, {\mathrm{ara}}^4}{{\left(\frac{181\, {\mathrm{ara}}^2}{81} + \frac{4525}{324}\right)}^2} + 1\right)}\right)}^2}{4} + \frac{{\left(\frac{2125764}{{\left(a + \frac{1}{10}\right)}^2} + \frac{729\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{2500} - \frac{{\left(\frac{7290000}{{\left(a + \frac{1}{10}\right)}^2} + {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2 + \frac{729}{2500}\right)}^2}{3} + \frac{7290000\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{{\left(a + \frac{1}{10}\right)}^2}\right)}^3}{27}} - \frac{1062882\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{{\left(a + \frac{1}{10}\right)}^2} + \frac{1250\, \left(\frac{4345080004734585\, r^8}{68719476736} + \frac{384160000\, a^4\, {\mathrm{ara}}^4}{{\left(\frac{181\, {\mathrm{ara}}^2}{81} + \frac{4525}{324}\right)}^2} + 1\right)}{a^2\, \left(\frac{21778071482940061661655974875633165533184\, r^8}{53817251171012308427455331739009} + \frac{10000\, a^4\, {\mathrm{ara}}^4}{{\left(\frac{181\, {\mathrm{ara}}^2}{81} + \frac{4525}{324}\right)}^2} + 1\right)}\right)}^{\frac{2}{3}}} - \frac{\frac{\left(\frac{2500\, \left(\frac{1536640000\, a^4\, {\mathrm{ara}}^3}{{\left(\frac{181\, {\mathrm{ara}}^2}{81} + \frac{4525}{324}\right)}^2} - \frac{278131840000\, a^4\, {\mathrm{ara}}^5}{81\, {\left(\frac{181\, {\mathrm{ara}}^2}{81} + \frac{4525}{324}\right)}^3}\right)}{a^2\, \left(\frac{21778071482940061661655974875633165533184\, r^8}{53817251171012308427455331739009} + \frac{10000\, a^4\, {\mathrm{ara}}^4}{{\left(\frac{181\, {\mathrm{ara}}^2}{81} + \frac{4525}{324}\right)}^2} + 1\right)} - \frac{2500\, \left(\frac{40000\, a^4\, {\mathrm{ara}}^3}{{\left(\frac{181\, {\mathrm{ara}}^2}{81} + \frac{4525}{324}\right)}^2} - \frac{7240000\, a^4\, {\mathrm{ara}}^5}{81\, {\left(\frac{181\, {\mathrm{ara}}^2}{81} + \frac{4525}{324}\right)}^3}\right)\, \left(\frac{4345080004734585\, r^8}{68719476736} + \frac{384160000\, a^4\, {\mathrm{ara}}^4}{{\left(\frac{181\, {\mathrm{ara}}^2}{81} + \frac{4525}{324}\right)}^2} + 1\right)}{a^2\, {\left(\frac{21778071482940061661655974875633165533184\, r^8}{53817251171012308427455331739009} + \frac{10000\, a^4\, {\mathrm{ara}}^4}{{\left(\frac{181\, {\mathrm{ara}}^2}{81} + \frac{4525}{324}\right)}^2} + 1\right)}^2}\right)\, \left(\frac{2\, {\left(\frac{7290000}{{\left(a + \frac{1}{10}\right)}^2} + {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2 + \frac{729}{2500}\right)}^3}{27} - \frac{\left(\frac{7290000}{{\left(a + \frac{1}{10}\right)}^2} + {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2 + \frac{729}{2500}\right)\, \left(\frac{2125764}{{\left(a + \frac{1}{10}\right)}^2} + \frac{729\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{2500} + \frac{7290000\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{{\left(a + \frac{1}{10}\right)}^2}\right)}{3} + \frac{2125764\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{{\left(a + \frac{1}{10}\right)}^2} - \frac{2500\, \left(\frac{4345080004734585\, r^8}{68719476736} + \frac{384160000\, a^4\, {\mathrm{ara}}^4}{{\left(\frac{181\, {\mathrm{ara}}^2}{81} + \frac{4525}{324}\right)}^2} + 1\right)}{a^2\, \left(\frac{21778071482940061661655974875633165533184\, r^8}{53817251171012308427455331739009} + \frac{10000\, a^4\, {\mathrm{ara}}^4}{{\left(\frac{181\, {\mathrm{ara}}^2}{81} + \frac{4525}{324}\right)}^2} + 1\right)}\right)}{4\, \sqrt{\frac{{\left(\frac{2\, {\left(\frac{7290000}{{\left(a + \frac{1}{10}\right)}^2} + {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2 + \frac{729}{2500}\right)}^3}{27} - \frac{\left(\frac{7290000}{{\left(a + \frac{1}{10}\right)}^2} + {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2 + \frac{729}{2500}\right)\, \left(\frac{2125764}{{\left(a + \frac{1}{10}\right)}^2} + \frac{729\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{2500} + \frac{7290000\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{{\left(a + \frac{1}{10}\right)}^2}\right)}{3} + \frac{2125764\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{{\left(a + \frac{1}{10}\right)}^2} - \frac{2500\, \left(\frac{4345080004734585\, r^8}{68719476736} + \frac{384160000\, a^4\, {\mathrm{ara}}^4}{{\left(\frac{181\, {\mathrm{ara}}^2}{81} + \frac{4525}{324}\right)}^2} + 1\right)}{a^2\, \left(\frac{21778071482940061661655974875633165533184\, r^8}{53817251171012308427455331739009} + \frac{10000\, a^4\, {\mathrm{ara}}^4}{{\left(\frac{181\, {\mathrm{ara}}^2}{81} + \frac{4525}{324}\right)}^2} + 1\right)}\right)}^2}{4} + \frac{{\left(\frac{2125764}{{\left(a + \frac{1}{10}\right)}^2} + \frac{729\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{2500} - \frac{{\left(\frac{7290000}{{\left(a + \frac{1}{10}\right)}^2} + {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2 + \frac{729}{2500}\right)}^2}{3} + \frac{7290000\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{{\left(a + \frac{1}{10}\right)}^2}\right)}^3}{27}}} - \frac{1250\, \left(\frac{1536640000\, a^4\, {\mathrm{ara}}^3}{{\left(\frac{181\, {\mathrm{ara}}^2}{81} + \frac{4525}{324}\right)}^2} - \frac{278131840000\, a^4\, {\mathrm{ara}}^5}{81\, {\left(\frac{181\, {\mathrm{ara}}^2}{81} + \frac{4525}{324}\right)}^3}\right)}{a^2\, \left(\frac{21778071482940061661655974875633165533184\, r^8}{53817251171012308427455331739009} + \frac{10000\, a^4\, {\mathrm{ara}}^4}{{\left(\frac{181\, {\mathrm{ara}}^2}{81} + \frac{4525}{324}\right)}^2} + 1\right)} + \frac{1250\, \left(\frac{40000\, a^4\, {\mathrm{ara}}^3}{{\left(\frac{181\, {\mathrm{ara}}^2}{81} + \frac{4525}{324}\right)}^2} - \frac{7240000\, a^4\, {\mathrm{ara}}^5}{81\, {\left(\frac{181\, {\mathrm{ara}}^2}{81} + \frac{4525}{324}\right)}^3}\right)\, \left(\frac{4345080004734585\, r^8}{68719476736} + \frac{384160000\, a^4\, {\mathrm{ara}}^4}{{\left(\frac{181\, {\mathrm{ara}}^2}{81} + \frac{4525}{324}\right)}^2} + 1\right)}{a^2\, {\left(\frac{21778071482940061661655974875633165533184\, r^8}{53817251171012308427455331739009} + \frac{10000\, a^4\, {\mathrm{ara}}^4}{{\left(\frac{181\, {\mathrm{ara}}^2}{81} + \frac{4525}{324}\right)}^2} + 1\right)}^2}}{3\, {\left(\sqrt{\frac{{\left(\frac{2\, {\left(\frac{7290000}{{\left(a + \frac{1}{10}\right)}^2} + {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2 + \frac{729}{2500}\right)}^3}{27} - \frac{\left(\frac{7290000}{{\left(a + \frac{1}{10}\right)}^2} + {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2 + \frac{729}{2500}\right)\, \left(\frac{2125764}{{\left(a + \frac{1}{10}\right)}^2} + \frac{729\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{2500} + \frac{7290000\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{{\left(a + \frac{1}{10}\right)}^2}\right)}{3} + \frac{2125764\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{{\left(a + \frac{1}{10}\right)}^2} - \frac{2500\, \left(\frac{4345080004734585\, r^8}{68719476736} + \frac{384160000\, a^4\, {\mathrm{ara}}^4}{{\left(\frac{181\, {\mathrm{ara}}^2}{81} + \frac{4525}{324}\right)}^2} + 1\right)}{a^2\, \left(\frac{21778071482940061661655974875633165533184\, r^8}{53817251171012308427455331739009} + \frac{10000\, a^4\, {\mathrm{ara}}^4}{{\left(\frac{181\, {\mathrm{ara}}^2}{81} + \frac{4525}{324}\right)}^2} + 1\right)}\right)}^2}{4} + \frac{{\left(\frac{2125764}{{\left(a + \frac{1}{10}\right)}^2} + \frac{729\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{2500} - \frac{{\left(\frac{7290000}{{\left(a + \frac{1}{10}\right)}^2} + {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2 + \frac{729}{2500}\right)}^2}{3} + \frac{7290000\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{{\left(a + \frac{1}{10}\right)}^2}\right)}^3}{27}} - \frac{{\left(\frac{7290000}{{\left(a + \frac{1}{10}\right)}^2} + {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2 + \frac{729}{2500}\right)}^3}{27} + \frac{\left(\frac{7290000}{{\left(a + \frac{1}{10}\right)}^2} + {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2 + \frac{729}{2500}\right)\, \left(\frac{2125764}{{\left(a + \frac{1}{10}\right)}^2} + \frac{729\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{2500} + \frac{7290000\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{{\left(a + \frac{1}{10}\right)}^2}\right)}{6} - \frac{1062882\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{{\left(a + \frac{1}{10}\right)}^2} + \frac{1250\, \left(\frac{4345080004734585\, r^8}{68719476736} + \frac{384160000\, a^4\, {\mathrm{ara}}^4}{{\left(\frac{181\, {\mathrm{ara}}^2}{81} + \frac{4525}{324}\right)}^2} + 1\right)}{a^2\, \left(\frac{21778071482940061661655974875633165533184\, r^8}{53817251171012308427455331739009} + \frac{10000\, a^4\, {\mathrm{ara}}^4}{{\left(\frac{181\, {\mathrm{ara}}^2}{81} + \frac{4525}{324}\right)}^2} + 1\right)}\right)}^{\frac{2}{3}}}\right)}{{\left({\left(\sqrt{\frac{{\left(\frac{2\, {\left(\frac{7290000}{{\left(a + \frac{1}{10}\right)}^2} + {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2 + \frac{729}{2500}\right)}^3}{27} - \frac{\left(\frac{7290000}{{\left(a + \frac{1}{10}\right)}^2} + {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2 + \frac{729}{2500}\right)\, \left(\frac{2125764}{{\left(a + \frac{1}{10}\right)}^2} + \frac{729\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{2500} + \frac{7290000\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{{\left(a + \frac{1}{10}\right)}^2}\right)}{3} + \frac{2125764\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{{\left(a + \frac{1}{10}\right)}^2} - \frac{2500\, \left(\frac{4345080004734585\, r^8}{68719476736} + \frac{384160000\, a^4\, {\mathrm{ara}}^4}{{\left(\frac{181\, {\mathrm{ara}}^2}{81} + \frac{4525}{324}\right)}^2} + 1\right)}{a^2\, \left(\frac{21778071482940061661655974875633165533184\, r^8}{53817251171012308427455331739009} + \frac{10000\, a^4\, {\mathrm{ara}}^4}{{\left(\frac{181\, {\mathrm{ara}}^2}{81} + \frac{4525}{324}\right)}^2} + 1\right)}\right)}^2}{4} + \frac{{\left(\frac{2125764}{{\left(a + \frac{1}{10}\right)}^2} + \frac{729\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{2500} - \frac{{\left(\frac{7290000}{{\left(a + \frac{1}{10}\right)}^2} + {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2 + \frac{729}{2500}\right)}^2}{3} + \frac{7290000\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{{\left(a + \frac{1}{10}\right)}^2}\right)}^3}{27}} - \frac{{\left(\frac{7290000}{{\left(a + \frac{1}{10}\right)}^2} + {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2 + \frac{729}{2500}\right)}^3}{27} + \frac{\left(\frac{7290000}{{\left(a + \frac{1}{10}\right)}^2} + {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2 + \frac{729}{2500}\right)\, \left(\frac{2125764}{{\left(a + \frac{1}{10}\right)}^2} + \frac{729\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{2500} + \frac{7290000\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{{\left(a + \frac{1}{10}\right)}^2}\right)}{6} - \frac{1062882\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{{\left(a + \frac{1}{10}\right)}^2} + \frac{1250\, \left(\frac{4345080004734585\, r^8}{68719476736} + \frac{384160000\, a^4\, {\mathrm{ara}}^4}{{\left(\frac{181\, {\mathrm{ara}}^2}{81} + \frac{4525}{324}\right)}^2} + 1\right)}{a^2\, \left(\frac{21778071482940061661655974875633165533184\, r^8}{53817251171012308427455331739009} + \frac{10000\, a^4\, {\mathrm{ara}}^4}{{\left(\frac{181\, {\mathrm{ara}}^2}{81} + \frac{4525}{324}\right)}^2} + 1\right)}\right)}^{\frac{1}{3}} + {\left(\frac{\left(\frac{7290000}{{\left(a + \frac{1}{10}\right)}^2} + {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2 + \frac{729}{2500}\right)\, \left(\frac{2125764}{{\left(a + \frac{1}{10}\right)}^2} + \frac{729\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{2500} + \frac{7290000\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{{\left(a + \frac{1}{10}\right)}^2}\right)}{6} - \frac{{\left(\frac{7290000}{{\left(a + \frac{1}{10}\right)}^2} + {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2 + \frac{729}{2500}\right)}^3}{27} - \sqrt{\frac{{\left(\frac{2\, {\left(\frac{7290000}{{\left(a + \frac{1}{10}\right)}^2} + {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2 + \frac{729}{2500}\right)}^3}{27} - \frac{\left(\frac{7290000}{{\left(a + \frac{1}{10}\right)}^2} + {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2 + \frac{729}{2500}\right)\, \left(\frac{2125764}{{\left(a + \frac{1}{10}\right)}^2} + \frac{729\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{2500} + \frac{7290000\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{{\left(a + \frac{1}{10}\right)}^2}\right)}{3} + \frac{2125764\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{{\left(a + \frac{1}{10}\right)}^2} - \frac{2500\, \left(\frac{4345080004734585\, r^8}{68719476736} + \frac{384160000\, a^4\, {\mathrm{ara}}^4}{{\left(\frac{181\, {\mathrm{ara}}^2}{81} + \frac{4525}{324}\right)}^2} + 1\right)}{a^2\, \left(\frac{21778071482940061661655974875633165533184\, r^8}{53817251171012308427455331739009} + \frac{10000\, a^4\, {\mathrm{ara}}^4}{{\left(\frac{181\, {\mathrm{ara}}^2}{81} + \frac{4525}{324}\right)}^2} + 1\right)}\right)}^2}{4} + \frac{{\left(\frac{2125764}{{\left(a + \frac{1}{10}\right)}^2} + \frac{729\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{2500} - \frac{{\left(\frac{7290000}{{\left(a + \frac{1}{10}\right)}^2} + {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2 + \frac{729}{2500}\right)}^2}{3} + \frac{7290000\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{{\left(a + \frac{1}{10}\right)}^2}\right)}^3}{27}} - \frac{1062882\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{{\left(a + \frac{1}{10}\right)}^2} + \frac{1250\, \left(\frac{4345080004734585\, r^8}{68719476736} + \frac{384160000\, a^4\, {\mathrm{ara}}^4}{{\left(\frac{181\, {\mathrm{ara}}^2}{81} + \frac{4525}{324}\right)}^2} + 1\right)}{a^2\, \left(\frac{21778071482940061661655974875633165533184\, r^8}{53817251171012308427455331739009} + \frac{10000\, a^4\, {\mathrm{ara}}^4}{{\left(\frac{181\, {\mathrm{ara}}^2}{81} + \frac{4525}{324}\right)}^2} + 1\right)}\right)}^{\frac{1}{3}}\right)}^2} $$ 事实上画出来就是ara对周期影响微乎其微. 我不知道为嘛是这样的.

if $$q==0$$ $$p>0 \Longrightarrow $$ 1个振动中心 此时周期==$$\frac{2\, \pi}{{\left(\frac{2125764}{{\left(a + \frac{1}{10}\right)}^2} + \frac{729\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{2500} - \frac{{\left(\frac{7290000}{{\left(a + \frac{1}{10}\right)}^2} + {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2 + \frac{729}{2500}\right)}^2}{3} + \frac{7290000\, {\left(\frac{2700}{\mathrm{auf} + \frac{1}{10}} + \frac{9}{10}\right)}^2}{{\left(a + \frac{1}{10}\right)}^2}\right)}^{\frac{1}{4}}} $$ 周期对于ara的导数==0 $$p \leq 0 \Longrightarrow $$ 0个振动中心