Fictitious Forces $\overset{?}{⇔}$ Constraint Forces (re: D'Alembert's Principle)

Are fictitious forces and constraint forces the same thing?

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No. I don't understand why you think there is any connection. – Siyuan Ren Sep 8 '12 at 2:22
@KarsusRen: This is probably a question on terminology, and your answer is adequate--- why not make it an answer, together with an example or two? – Ron Maimon Sep 8 '12 at 3:09

2 Answers

There are not the same thing. Fictitious forces usually arise because of change of co-ordinates, e.g. to a rotating frame. They are terms added to make the whole equation look like a vector sum of forces. The constraint forces are very real, and arise due to geometrical constraints, such as motion along a plane gives rise to the normal force produced by the plane, or the constancy of the length of a string tied to a pendulum gives rise to the tension.

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How can geometry produce forces? Something else must be responsible for constraint forces. – Geremia Sep 8 '12 at 17:27

The question is legitimate in the sense that one can often read, especially in older literature, that "d'Alembert's Principle has successfully reduced Dynamics to Statics". If d'Alembert's Principle (principle of virtual work) stated for a constrained system in equilibrium $$\sum_k{F_k\ \delta r_k =0}$$ is enough to lay the foundations of Statics (bridges, buildings) then it is a remarcable result that the very same principle would completely suffice for Dynamics.

In this case then the $- m \dot v$ addition to the principle are really nothing more than the fictitious forces appearing in the comoving frame where the representative point is at equilibrium (pure statics).

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Now I see that the question was asked about the constraint forces. Obviously these are not the fictive forces (which do indeed apear in this setting) but they are simply the difference between the real and the fictitious (forces of inertia) forces, $F_{constraint}=F-m\ \dot v$ – Lupercus Sep 8 '12 at 11:03
Yes, D'Alembert's Principle interpreted as a reduction of dynamics to statics is exactly what prompted my question. – Geremia Sep 8 '12 at 17:49