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phantomvommand

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Is energy always conserved in a co-rotating/accelerating frame?

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- Thread starter phantomvommand
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- #1

phantomvommand

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Is energy always conserved in a co-rotating/accelerating frame?

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Dale

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ergospherical

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For other systems, whether or not you can find energy integrals depends on whether there is time dependence in the lagrangian i.e. write ##H = \dot{q}^i \dfrac{\partial L}{\partial \dot{q}^i} - L## then if ##\partial L/\partial t=0## you have$$\dfrac{dH}{dt} = \dot{q}^i \dfrac{d}{dt} \dfrac{\partial L}{\partial \dot{q}^i} + \dfrac{\partial L}{\partial \dot{q}^i} \ddot{q}^i - \dfrac{\partial L}{\partial q^i} \dot{q}^i - \dfrac{\partial L}{\partial \dot{q}^i} \ddot{q}^i$$which equals zero.

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