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- Thread starter Kolahal Bhattacharya
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so what?What has that to do with the virtual work?

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I think the other constraint force is the wedge against the block.

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Forces of constraint can do work if they're time dependent. This is a rather important point.

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If you think about constraint... Well, what is a constraint, really? a constraint is a function relating a constant to variables. for example, assuming time independence:

[tex]f(q_1,q_2)=C[/tex]

the constraint force is the gradient of f, which is always orthogonal to the level surface described by the constraint, hence,

[tex]\vec{\nabla} f\cdot{d\vec{r}}=0[/tex]

you can think of constraint force as a force that keeps a system in the level "surface" described by the constraint, so that the constraint force has to be orthogonal to that "surface" thus the work done by the constraint force is zero.

just a note: in my book, the definition of constraint force is implicitly stated as "the force that does no work"...it is just a stated fact.

[tex]f(q_1,q_2)=C[/tex]

the constraint force is the gradient of f, which is always orthogonal to the level surface described by the constraint, hence,

[tex]\vec{\nabla} f\cdot{d\vec{r}}=0[/tex]

you can think of constraint force as a force that keeps a system in the level "surface" described by the constraint, so that the constraint force has to be orthogonal to that "surface" thus the work done by the constraint force is zero.

just a note: in my book, the definition of constraint force is implicitly stated as "the force that does no work"...it is just a stated fact.

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[tex]f(q_1,q_2)=C[/tex]

the constraint force is the gradient of f, which is always orthogonal to the level surface described by the constraint, hence,

[tex]\vec{\nabla} f\cdot{d\vec{r}}=0[/tex]

you can think of constraint force as a force that keeps a system in the level "surface" described by the constraint, so that the constraint force has to be orthogonal to that "surface" thus the work done by the constraint force is zero.

just a note: in my book, the definition of constraint force is implicitly stated as "the force that does no work"...it is just a stated fact.

But as I said earlier, there are some constraints that do actually do work. Look at the bead on a loop problem. You can view it as being the constraint that [tex]\theta = \omega t + \theta_0[/tex], but it's most definitely doing work. Energy is not conserved in that case. Thankfully, it's an holonomic constraint, but it is adding energy to the system none the less.

Constraints arise from forces that cannot be classified easily as potentials, but which don't necessarily act except in a way to force the particle to behave within a certain set of parameters. If I have a mass on a track and constrain it to that track, there's a normal force keeping it on the track, but it's much easier to simply state that the particle has to be along this track than to characterize the normal forces, and this is one of the great power of lagrangian mechanics over straight Newtonian mechanics.

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