Equations

$m_i\frac{\text{d}{u}_i}{\text{d}t}=m_{i}g+F_p+{\displaystyle \sum _{i=1}^n{F}_{c,ij}}$

(1)

$I_i\frac{\text{d}{\omega }_i}{\text{d}t}=T_r+{\displaystyle \sum _{i=1}^n{T}_{ij}}$

(2)

$F_{c,ij}=F_{c,ij}^n+F_{c,ij}^t=\left(k_n{\delta }_{nij}n-{\gamma }_n{v}_{nij}\right)+\left(k_t{\delta }_{tij}t-{\gamma }_t{v}_{tij}\right)$

(3)

$k_n=\frac{4}{3}{Y}^{*}\sqrt{R^{*}{\delta }_n}{k}_t=8G^{*}\sqrt{R^{*}{\delta }_n}$

(4)

${\Gamma }_n=-2\sqrt{\frac{5}{6}}\zeta \sqrt{k_n{m}^{*}}$

(5)

${\gamma }_t=-2\sqrt{\frac{5}{6}}\zeta \sqrt{k_t{m}^{*}}$

(6)

$\zeta =\frac{\ln \left(e\right)}{\sqrt{{\ln }^2\left(e\right)+{\pi }^2}}$

(7)