Лагранжиан гравитационного поля

Last modified by Alexey Popov on 2019/02/04 16:19

$\mathcal L = \frac{kg }{s^2 \, m^3}\mathbf r^2 + \frac{kg }{m^3}\mathbf v^2 + \frac{kg \,s^2}{m^3}\mathbf a^2 + \frac{kg \,s^4}{m^3}\mathbf j^2+\frac{kg \,s^6}{m^3}\mathbf s^2 +$

$\mathcal L = \rho_r\mathbf r^2 + \rho\mathbf v^2 + \rho_a\mathbf a^2 + \rho_j\mathbf j^2+\rho_s\mathbf s^2 +$

$+\rho_r r_c^2 + \rho c^2 + \rho_a a_c^2 + \rho_j j_c^2+\rho_s s_c^2 +$

$+\rho_{rn}\mathbf r^2 + \rho_{n}\mathbf v^2 + \rho_{an}\mathbf a^2 + \rho_{jn}\mathbf j^2+\rho_{sn}\mathbf s^2 +$

$+\rho_{rn}r_c^2 + \rho_{n}c^2 + \rho_{an}a_c^2 + \rho_{jn}j_c^2+\rho_{sn}s_c^2$

$\mathcal L(\Phi(\mathbf x,t))=-\rho_n\frac{\Phi(\mathbf x,t)^2}{c^2}+\frac{\rho(\mathbf x,t)^2}{\rho_n}\Phi(\mathbf x,t)+\rho_n\Phi(\mathbf x,t)+\frac{\rho(\mathbf x,t)^2\mathbf v_s(\mathbf x,t)^2}{\rho_n c^2}\Phi(\mathbf x,t)+\frac{\rho_n\mathbf v_s(\mathbf x,t)^2}{ c^2}\Phi(\mathbf x,t)- \frac{w(\mathbf x,t)^2}{\rho_n c^4}\Phi(\mathbf x,t)$

$0=-\rho_n\frac{\Phi(\mathbf x,t)}{c^2}+\frac{\rho(\mathbf x,t)^2}{\rho_n}+\rho_n+\frac{\rho(\mathbf x,t)^2\mathbf v_s(\mathbf x,t)^2}{\rho_n c^2}+\frac{\rho_n\mathbf v_s(\mathbf x,t)^2}{c^2}- \frac{w(\mathbf x,t)^2}{\rho_n c^4}$

$\Phi(\mathbf x,t)=c^2\frac{\rho(\mathbf x,t)^2}{ \rho_n^2}+c^2+\frac{\rho(\mathbf x,t)^2\mathbf v_s(\mathbf x,t)^2}{\rho_n^2 }+\mathbf v_s(\mathbf x,t)^2- \frac{w(\mathbf x,t)^2}{\rho_n^2 c^2}$

$w(\mathbf x,t) = \frac{\rho_n}{e} c^2$

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Created by Alexey Popov on 2018/09/05 10:52