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The D'Alembert's Principle states that:

[itex] \sum_s [\underline{ F_s^{applied}} - \frac{d}{dt} (\underline{p_s}) ] \cdot \underline{δr_s} = 0 [/itex]

s - labels particles

That is when [itex] F_s [/itex] doesn't include the constraint forces, and the virtual displacement is reversible, and compatible with the constraints.

My question is - doesn't it just say that:

- if there are no constraints, Newton's laws are obeyed, with force being [itex] F_s [/itex] - (the parenthesis is zero)

- if there are holonomic constraints, we can only displace the object perpendicular to the constraint forces - (the dot product is zero)

?

Does this principle also say something about non-holonomic constraints? And if so, can anyone give an example?

And what exactly is the difference between reversible and irreversible virtual displacement? If a displacement is virtual, and if displacing by dx is possible, then also displacing back by -dx should be possible. So how can we have an irreversible displacement at all?

[itex] \sum_s [\underline{ F_s^{applied}} - \frac{d}{dt} (\underline{p_s}) ] \cdot \underline{δr_s} = 0 [/itex]

s - labels particles

That is when [itex] F_s [/itex] doesn't include the constraint forces, and the virtual displacement is reversible, and compatible with the constraints.

My question is - doesn't it just say that:

- if there are no constraints, Newton's laws are obeyed, with force being [itex] F_s [/itex] - (the parenthesis is zero)

- if there are holonomic constraints, we can only displace the object perpendicular to the constraint forces - (the dot product is zero)

?

Does this principle also say something about non-holonomic constraints? And if so, can anyone give an example?

And what exactly is the difference between reversible and irreversible virtual displacement? If a displacement is virtual, and if displacing by dx is possible, then also displacing back by -dx should be possible. So how can we have an irreversible displacement at all?

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