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Problem 2 rigid rods - Greenwood - Classical Dynamics

  1. Oct 22, 2015 #1
    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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  2. jcsd
  3. Oct 22, 2015 #2

    BvU

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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) 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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    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 ...
     
    Last edited: Oct 22, 2015
  4. Oct 22, 2015 #3
    Yes, that one.
    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.
    Can't understand: the rods lengths are constant, but their horizontal projections are not, even with the "small motions" he asks to assume.
    Meanwhile, thank you for your answer.
    Waiting for your next reply.

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