Ah okay, so basically Lagranges Equations originally come from d'alemberts Principle and not from the Hamilton Principle, the Hamilton Principle is only a consequence of Lagranges Interpretation of Mechanics? Have I understood that right, therefore the Hamilton Principle is always just given...
Okay thanks guys I think I have undertstood better now. But do you have any Papers or Books where I specificely could read something directly about how to derive Hamiltons Principle, so how to derive that ##\delta \int L \; dt## (A), not how to get from Hamiltons Principle to the equations of...
Thanks for your answer.
Now the thing I do not understand is how to even derive the LHS from equation (4) (in the paper). Even if we look at your explanation we still take the Hamilton Principle
##\delta \int L \; dt = 0##
for granted and just put in equation (4). But to derive the Hamilton...
I have recently been really interested in the derivation of Hamiltons Principle. On my research I found that with the term
##m \cdot \frac{d}{dt} (\frac{dr}{dt} \cdot \delta r) = 0## (1) one may derivate ##\delta \int (T - V) dt = 0## (2). The derivation itself I understood quiet good, but what...