Problem 2 rigid rods - Greenwood - Classical Dynamics

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From "Greenwood Donald T. - Classical Dynamics", Chapter 1, Section 1-4 (virtual work), Example 1-4:

https://books.google.it/books?id=x7rj83I98yMC&lpg=PP1&hl=it&pg=PA26#v=onepage&q&f=false

1) There are 3 mass points of the same mass m moving on a plane (even if the text doesn't specify this) and 2 constraints given by the two rods, so the degrees of freedom should be 2*3 - 2 = 4, not 3 as the text suggests (since it uses only 3 coordinates). Why? It has to do with the fact the horizontal distances between the mass point 1 and 2 and between 2 and 3 are the same = l, as in figure 1-8? Why the system cannot move horizontally? Which exactly are the constraints in this system?

2) I can't understand his first method to compute the generalized forces Q1, Q2, Q3, which ends with equations (1-77) and (1-78) (I have understood the subsequent method but not this). How does he do exactly?

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That would be page 26 ? At first I got page limit reached in Italian, later on I did get the picture. funny.

1a) There are 3 mass points of the same mass m moving on a plane (even if the text doesn't specify this) and 2 constraints given by the two rods, so the degrees of freedom should be 2*3 - 2 = 4, not 3 as the text suggests (since it uses only 3 coordinates). Why?

1b) It has to do with the fact the horizontal distances between the mass point 1 and 2 and between 2 and 3 are the same = l, as in figure 1-8?

1c) Why the system cannot move horizontally? Which exactly are the constraints in this system?

1a) You are right but they don't care about the horizontal position, apparently.

1b) No, that are the two constraints and they do use them

1c) It can move horizontally, but with the two constraints two of these coordinates disappear and for the third see 1a).

The generalization has a physical meaning (fig 1-9): q₁ is the center of mass, q₃ = q₁ - x₂ or the "bending" and q₂ is the "tiliting".

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2) I can't understand his first method to compute the generalized forces Q1, Q2, Q3, which ends with equations (1-77) and (1-78) (I have understood the subsequent method but not this). How does he do exactly?

Donald uses the definition of generalized forces (1-73 on page 24).

But I suppose you already found that. Is there a 'deeper' question ?

[edit] Not a good reply, I realize upon further reading in Greenwood. 1-73 is the second method he describes. So apparently he has a direct line from $\delta q$ to $\delta W$. Let me chew on that ...

 

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That would be page 26 ?

Yes, that one.

1a) You are right but they don't care about the horizontal position, apparently.

I see; do you think it depends just on the fact the applied force and momentum don't make virtual work along the horizontal direction? Anyway it's quite unusual for me.

1b) No, that are the two constraints and they do use them

Can't understand: the rods lengths are constant, but their horizontal projections are not, even with the "small motions" he asks to assume.

1c) It can move horizontally, but with the two constraints two of these coordinates disappear and for the third see 1a).
The generalization has a physical meaning (fig 1-9): q₁ is the center of mass, q₃ = q₁ - x₂ or the "bending" and q₂ is the "tilting".
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Donald uses the definition of generalized forces (1-73 on page 24).
But I suppose you already found that. Is there a 'deeper' question ?

[edit] Not a good reply, I realize upon further reading in Greenwood. 1-73 is the second method he describes. So apparently he has a direct line from $\delta q$ to $\delta W$. Let me chew on that ...

Meanwhile, thank you for your answer.
Waiting for your next reply.

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