27.Фуко

$\tiny m\vec{W}=\vec{P}+\vec{N}+\vec{I_{kor}}\\ \left\{\begin{matrix} m\ddot{x}=-N\frac{x}{l}+2m\omega \dot{y}sin\varphi\\ m\ddot{y}=-N\frac{y}{l}-2m\omega(\dot{z}cos\varphi+\dot{x}sin\varphi)\\ m\ddot{z}=-mg-N\frac{z}{l}+2m\omega\dot{y}cos\varphi \end{matrix}\right.\\ |x|<<l, |y|<<l; => z=-l\sqrt{1-\frac{x^2+y^2}{l^2}}\simeq -l, N=mg;\\ \ddot{x}=-\frac{gx}{l}+2\omega \dot{y}sin\varphi, \ddot{y}=-\frac{gy}{l}-2\omega\dot{x}sin\varphi\\ y\ddot{x}-x\ddot{y}=2\omega sin\varphi (y\dot{y}+x\dot{x})\\ y\dot{y}+x\dot{x}=\frac{1}{2}\frac{d}{dt}(x^2+y^2)=\frac{1}{2}\frac{d\rho^2}{dt}, y\ddot{x}-x\ddot{y}=-\frac{d}{dt}(x\dot{y}-y\dot{x})\\ x=\rho cos\Theta , y=\rho sin\Theta, => \dot{x}=..., \dot{y}=...\\$