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Book: Variational Principles of Mechanics by Lanczos, 1st edition, 1949.

Statement (page 80):

"Two systems of forces which produce the same virtual displacements are dynamically equivalent."

I don't understand the part about forces producing virtual displacements. I think of virtual displacements as infinitesimal variations from a path between two points on the configuration space. But these variations are arbitrary. How are the forces, which are certainly not arbitrary, producing these virtual displacements?

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In the 4th edition from 1970 the quoted sentence on p. 80 was changed to:

Two systems of forces which produce the same virtual work are dynamically equivalent.

This means in particular that we can ignore forces associated with zero virtual work, cf. the principle of virtual work and d'Alembert's principle.

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