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so today in maths we defined the Lagrangian as [tex]L = T-V[/tex] and stated Hamilton's Principle, which says that the actual path of a conservative system is the one which minimises the action

[tex]A(q)=\int^{t_{2}}_{t_{1}}L dt[/tex].

I'm a bit confused about this. What does the action represent in physical terms? Also, why on Earth would minimising the integral of [tex]L=T-V[/tex] result in the path which nature 'chooses'? How did Hamilton come up with this and why do we think it works (other than the fact it agrees with experiments!)?

Many thanks :D

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# Action and the Lagrangian

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