2.ДУ движения МТ

$\tiny m=const: m\vec{W}=\vec{F}\\ m\ddot{r}=\vec{F}(t,\vec{w},\vec{\upsilon})\\ \left\{\begin{matrix} m\ddot{x}=F_{x}(t,x,y,z,\dot{x},\dot{y},\dot{z})\\ m\ddot{y}=F_{y}(t,x,y,z,\dot{x},\dot{y},\dot{z})\\ m\ddot{z}=F_{z}(t,x,y,z,\dot{x},\dot{y},\dot{z}) \end{matrix}\right.\\ \tiny \left\{\begin{matrix} x=x(t,c_{1},...,c_{6})\\ y=y(t,c_{1},...,c_{6})\\ z=z(t,c_{1},...,c_{6}) \end{matrix}\right.\\ \tiny t=0: \vec{r}=\vec{r_{0}}, \vec{\upsilon}=\vec{\upsilon_{0}}, \dot{x}=\dot{x_{0}}, \dot{y}=\dot{y_{0}}, \dot{z}=\dot{z_{0}}\\ \tiny \tiny \left\{\begin{matrix} \dot{x}=\dot{x}(t,c_{1},...,c_{6})\\ \dot{y}=\dot{y}(t,c_{1},...,c_{6})\\ \dot{z}=\dot{z}(t,c_{1},...,c_{6}) \end{matrix}\right.\\ \tiny \left\{\begin{matrix} x=x(0,c_{1},...,c_{6})\\ y=y(0,c_{1},...,c_{6})\\ z=z(0,c_{1},...,c_{6})\\ \dot{x}=\dot{x}(0,c_{1},...,c_{6})\\ \dot{y}=\dot{y}(0,c_{1},...,c_{6})\\ \dot{z}=\dot{z}(0,c_{1},...,c_{6}) \end{matrix}\right.\\$

$\tiny C_{i}=C{i}(t,x_{0},y_{0},z_{0},\dot{x_{0}},\dot{y_{0}},\dot{z_{0}}), i=1,6\\ \tiny \begin{matrix} x=x(t,x_{0},y_{0},z_{0},\dot{x_{0}},\dot{y_{0}},\dot{z_{0}})\\ y=y(t,x_{0},y_{0},z_{0},\dot{x_{0}},\dot{y_{0}},\dot{z_{0}})\\ z=z(t,x_{0},y_{0},z_{0},\dot{x_{0}},\dot{y_{0}},\dot{z_{0}}) \end{matrix}\right. \\ \vec{r}=\vec{r}(t,\vec{r_{0}},\vec{\upsilon_{0}})\\ \tiny \int_{k}(t,x_{0},y_{0},z_{0},\dot{x_{0}},\dot{y_{0}},\dot{z_{0}})=C_{k}, k=1,6\\ \tiny m\ddot{r}=\vec{F}+\vec{N}\\$

$\tiny \left\{\begin{matrix} \tau: m\frac{d\upsilon}{dt}=F_{\tau}\\ n: m\frac{v}{\rho}=F_{n}+N_{n}\\ b:0=F_{b}+N_{b} \end{matrix}\right.$