İmpuls momentı: юрамалар арасында аерма

: <math>\mathbf{L}_{\mathrm{system}} = \mathrm{constant} \leftrightarrow \sum \tau_{\mathrm{ext}} = 0, </math>

 

 

<math>\delta \mathcal L = \mathcal L(\mathbf{r}_i + \delta\mathbf{r}_i,\; \mathbf{v}_i + \delta\mathbf{v}_i) - \mathcal L(\mathbf{r}_i,\; \mathbf{v}_i) = \sum \limits_i \left( \frac{\partial \mathcal L}{\partial \mathbf r_i} \delta \varphi \times\mathbf r_i + \frac{\partial \mathcal L}{\partial \mathbf v_i} \delta \varphi \times \mathbf v_i \right)= 0. </math>

:<math>\delta \mathcal L = \delta \varphi \sum \limits_i \left( \mathbf r_i \times \dot {\mathbf p_i} + \dot {\mathbf r_i} \times \mathbf p_i \right) = \delta \varphi \frac{d}{dt} \sum \limits_i (\mathbf r_i \times \mathbf p_i) = \delta \varphi \frac{d \mathbf L}{dt} = 0, </math>

 

Orbitada:

: <math>\mathbf{L}_{\mathrm{total}} = \mathbf{L}_{\mathrm{spin}} + \mathbf{L}_{\mathrm{orbit}}

.</math>