- #1

Kashmir

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Goldstein 2ed pg 36

So in the case of holonomic constraints we can move back and forth between Hamiltons principle and Lagrange equations given as ##\frac{d}{d t}\left(\frac{\partial L}{\partial \dot{q}_{j}}\right)-\frac{\partial L}{\partial q_{j}}=0##

But the Lagrange equations were derived from DAlembets principal Assuming that the virtual work of constraints is zero. But in the Hamilton‘s principal, we don’t see that the constraints should be workless .

Is it implicitly assumed that the virtual work of constraints is zero in Hamilton‘s principal?

How can we prove it?

So in the case of holonomic constraints we can move back and forth between Hamiltons principle and Lagrange equations given as ##\frac{d}{d t}\left(\frac{\partial L}{\partial \dot{q}_{j}}\right)-\frac{\partial L}{\partial q_{j}}=0##

But the Lagrange equations were derived from DAlembets principal Assuming that the virtual work of constraints is zero. But in the Hamilton‘s principal, we don’t see that the constraints should be workless .

Is it implicitly assumed that the virtual work of constraints is zero in Hamilton‘s principal?

How can we prove it?

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