Что такое гравитация

Last modified by Alexey Popov on 2019/08/15 19:01

$\varphi = \varepsilon_0\square (\mathbf r \times (\mathbf r \times \mathbf M))^2 + \mu_0\square (\mathbf r \times (\mathbf r \times \mathbf J))^2$

$\varphi = \varepsilon_0\square \boldsymbol{\mathcal M}^2+ \mu_0 \square \mathbf A^2 = w$

$\mathbf a = - \frac{1}{\rho_n}\nabla w - \frac{1}{\rho_n c^2}\frac{\partial w\mathbf v}{\partial t} - \frac{1}{\rho_n c^2}\frac{\partial^2 w\mathbf r}{\partial t^2}$

$E = m c^2$

$\frac{E}{V} = \frac{m}{V} c^2$

$\frac{E}{V} = w$

$\frac{m}{V}= \rho$

$w = \rho c^2$

$w_{ke} = \frac{1}{2}\rho v^2$

$\rho_n = m_n \frac{1}{V_n}= m_n(\frac{3 \pi}{4} \frac{m_n c}{h})^3$

$w_n = \rho_n c^2 = const$

$w_{pe} = \frac{1}{2}\rho_n v^2$

$\mathcal{L} = w_{ke} + w_{pe} - w - w_n$

$\nabla \mathcal{L} - \frac{\partial }{\partial t}\frac{\partial \mathcal{L}}{\partial v} = 0$

$\mathcal{L} = \frac{1}{2}\rho v^2 + \frac{1}{2}\rho_n v^2 - \rho c^2 - \rho_n c^2$

$\frac{\partial \mathcal{L}}{\partial v} = \rho v + \rho_n v$

$\nabla \mathcal{L} - \frac{\partial }{\partial t}\frac{\partial \mathcal{L}}{\partial v} = \frac{1}{2}\nabla (\rho v^2) + \frac{1}{2}\rho_n \nabla v^2 - c^2 \nabla \rho - \frac{\partial \rho v}{\partial t} - \rho_n \frac{\partial v}{\partial t} = 0$

$\frac{1}{2}\frac{1}{\rho_n}\nabla (\rho v^2) + \frac{1}{2} \nabla v^2 - c^2\frac{1}{\rho_n} \nabla \rho - \frac{1}{\rho_n}\frac{\partial \rho v}{\partial t} - \frac{\partial v}{\partial t} = 0$

$\frac{1}{2}\frac{1}{\rho_n}\nabla (\rho v^2) + \frac{1}{2} \nabla v^2 = c^2\frac{1}{\rho_n} \nabla \rho$

$v^2 \ll c^2$

$\frac{1}{2} \nabla v^2 = c^2\frac{1}{\rho_n} \nabla \rho$

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Created by Alexey Popov on 2019/08/07 14:27