Th об изменении кол-ва движения мт. 1-ый интеграл

$\tiny \frac{d}{dt}(m\vec{\upsilon})=\vec{F}\\ d(m\vec{\upsilon})=\vec{F}dt$ -элементарный импульс силы

$\tiny \left\{\begin{matrix} d(m\ddot{x})=F_{x}dt\\ d(m\ddot{y})=F_{y}dt\\ d(m\ddot{z})=F_{z}dt\\ \end{matrix}\right.\\ \tiny \int_{\upsilon_{0}}^{\upsilon}m\vec{\upsilon}d\upsilon=\int_{0}^{t}\vec{F}dt\\ m\vec{\upsilon}-m\vec{\upsilon_{0}}=\int_{0}^{t}\vec{F}dt\\ \tiny \left\{\begin{matrix} m\dot{x}-m\dot{x_{0}}=\int_{0}^{t}\F_{x}dt\\ m\dot{y}-m\dot{y_{0}}=\int_{0}^{t}\F_{y}dt\\ m\dot{z}-m\dot{z_{0}}=\int_{0}^{t}\F_{z}dt \end{matrix}\right.\\ \tiny F=0 => \upsilon=const;\\ F_{x}=F_{y}=0 => \dot{x}=C_{1}, \dot{y}=C_{2} => C_{1}\dot{y}-C_{2}\dot{x}=0 => C_{1}y-C_{2}x=C_{3} \\ F_{z}=0 => \dot{z}=const;\\$

$\tiny F=0 => \upsilon=const;\\ F_{x}=F_{y}=0 => \dot{x}=C_{1}, \dot{y}=C_{2} => C_{1}\dot{y}-C_{2}\dot{x}=0 => C_{1}y-C_{2}x=C_{3} \\ F_{z}=0 => \dot{z}=const;$