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Appendix 2: D’Alembert’s Principle
and Lagrange’s Equations
A2.1 VIRTUAL DISPLACEMENT, VIRTUAL WORK,
AND PRINCIPLE OF VIRTUAL WORK
D’Alembert’s principle is based on the concepts of virtual displacement and virtual work. What do
we mean by virtual displacement and virtual work?
a2.1.1 virTual disPlacemenT
A virtual displacement, denoted by δr
1
,
is dened as an imagined, innitesimal, instantaneous dis-
placement of the coordinates that is consistent with the constraints. In other words, virtual displace-
ments have three characteristics: (1) They are innitesimal, (2) they occur at a given instant in time
(i.e., no time changes δt = 0), and ...