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henpen
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Lagrangian mechanics: Is the definition \[\frac{\partial \mathbf{U}}{\partial \mathbf{x}}=\mathbf{F}\] arrived at only by minimising action (that is, using the EulerLagrange equation) and F=ma (that is, is there any other equally thorough way of doing it)?
 one year ago
 one year ago
henpen Group Title
Lagrangian mechanics: Is the definition \[\frac{\partial \mathbf{U}}{\partial \mathbf{x}}=\mathbf{F}\] arrived at only by minimising action (that is, using the EulerLagrange equation) and F=ma (that is, is there any other equally thorough way of doing it)?
 one year ago
 one year ago

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henpen Group TitleBest ResponseYou've already chosen the best response.0
That is, if you assume \[T=0.5m\dot{x}^2\] and \[U=U\] , and plug this into the EulerLagrange equation (and Newton's 2nd law), you get \[m \ddot{x}=F=\frac{\partial \mathbf{U}}{\partial \mathbf{x}}\] . Is this the only fundamental way to get to this equation, or is it only one example of many equally fundamental ones?
 one year ago

henpen Group TitleBest ResponseYou've already chosen the best response.0
Also is the relation derivable *not* assuming \[T=0.5m\dot{x}^2\]?
 one year ago
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