- #1
sams
Gold Member
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Is there any proof for the Lagrangian:
$$L = T - U $$
And why L = T - U ?
Any help is much appreciated. Thank you.
$$L = T - U $$
And why L = T - U ?
Any help is much appreciated. Thank you.
Is there any physical explanation why L = T - U? Why we have the negative sign in the Lagrangian equation in U?What do you mean by proof? Lagrangian mechanics is a physics theory just as Newtonian mechanics. You don’t prove it, you test it experimentally.
Because if you put in a positive sign, you don't get the right (i.e. agree with experiment) answers.Why we have the negative sign in the Lagrangian equation in U?
The negative sign can be thought of as resulting from the assumption that the forces acting on the object can be expressed as the negative of the gradient of a scalar potential. If you follow the derivation of Lagrangian equations from Newton's laws it is quite clear. For example:Is there any physical explanation why L = T - U? Why we have the negative sign in the Lagrangian equation in U?
This follows from the 2nd Newton Law +hypothesis that the constraints are ideal and holonomic +hypothesis that the forces are potentialIs there any proof for the Lagrangian:
$$L = T - U $$
And why L = T - U ?
Any help is much appreciated. Thank you.