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theorems:liouvilles_theorem

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theorems:liouvilles_theorem [2018/05/06 14:04]
ida [Intuitive]
theorems:liouvilles_theorem [2018/07/04 12:35]
jakobadmin [Concrete]
Line 109: Line 109:
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-Now, if $\rho$ is constant $\frac{\partial ​\rho }{\partial ​t}= 0$, then the left-hand side is $0$ and we get:+Now, if $\rho$ is constant $\frac{\rho }{t}= 0$, then the left-hand side is $0$ and we get:
  
 $$\frac{\partial \rho }{\partial t}= -\sum_{i}\left(\frac{\partial \rho}{\partial q_i}\,​\dot{q_i}+\frac{\partial\rho}{\partial p_i}\,\dot p_i\right).$$ $$\frac{\partial \rho }{\partial t}= -\sum_{i}\left(\frac{\partial \rho}{\partial q_i}\,​\dot{q_i}+\frac{\partial\rho}{\partial p_i}\,\dot p_i\right).$$
theorems/liouvilles_theorem.txt · Last modified: 2019/03/05 15:07 by 129.13.36.189