Horizontal generator of contact stability
= Horizontal generator of contact stability
{title2=$(\iota_{Y_t}d\alpha_t)|_{\xi_t}=-\dot\alpha_t|_{\xi_t}$}
For a family of <contact forms>, require $Y_t\in\ker\alpha_t$ and solve $(\iota_{Y_t}d\alpha_t)|_{\ker\alpha_t}=-\dot\alpha_t|_{\ker\alpha_t}$. The <contact distribution symplectic form> gives a unique smooth solution. Then $\dot\alpha_t+\mathcal L_{Y_t}\alpha_t=h_t\alpha_t$, with $h_t=\dot\alpha_t(R_t)$ and $R_t$ the <Reeb vector field>.