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### D'Alembert's Principle: Necessity of virtual displacements

Why is the d'Alembert's Principle $$\sum_{i} ( {F}_{i} - m_i \bf{a}_i )\cdot \delta \bf r_i = 0$$ stated in terms of "virtual" displacements instead of actual displacements? Why is it so necessary ...
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### What type of displacement is virtual displacement? Is it really a displacement? How to calculate it? [duplicate]

Searched this question a lot in different places but could not find any answer that could satisfy me. So I am here to clear my concepts regarding virtual displacement. Now I am clarifying my doubt. As ...
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### D'Alembers Principle - further explanation [duplicate]

In question : Why is the d'Alembert's Principle formulated in terms of virtual displacements rather than real displacements in time? there is a response : ...
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### Are there examples in classical mechanics where D'Alembert's principle fails?

D'Alembert's principle suggests that the work done by the internal forces for a virtual displacement of a mechanical system in harmony with the constraints is zero. This is obviously true for the ...
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### Why can't d'Alembert's Principle be derived from Newton's laws alone?

The wiki article states that D'Alembert's Principle cannot derived from Newton's Laws alone and must stated as a postulate. Can someone explain why this is? It seems to me a rather obvious principle.
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### What is the definition of how to count degrees of freedom?

This question resulted, rather as by-product, the discussion on how to count degrees of freedom (DOF). I extend that question here: Are necessary1 derivatives such as velocities counted as individual ...
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