All Questions
15
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Vanishing virtual work done by non-holonomic constraints
I was reading classical mechanics by NC Rana. I was reading a topic on vanishing virtual work done due to constraint forces. How do you prove that the virtual work done by non-holonomic constraint ...
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0
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Aren't the virtual work/virtual power principles in mechanics simply solving for the vector differential equation of motion in a preferred direction?
My conceptual understanding of the virtual work/virtual power principles is that, by hypothesizing "virtual displacements"/"virtual velocities", one can solve the equations of ...
1
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1
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98
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Can Lagrange's equation be used if the virtual work done by constraint forces is not zero?
I'm learning analytical mechanics and was just introduced to d’Alembert’s principle, which I know is only valid when constraint forces' virtual work is zero. My question is, does this restriction also ...
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4
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Work done by constraint forces -- Generalisation
Consider the above scenario: In the subsequent motion, we need to find the work done by tension on the (trolley + mass) system.
Solution: Suppose at an instant, the velocity of the trolley (and hence ...
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1
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The "coefficients" of virtual displacement in Goldstein's classical mechanics
In Goldstein's classical mechanics the following passage is confusing me:
We therefore have as the condition for equilibrium of a system that the virtual work of the applied forces vanishes: $$\sum_i ...
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2
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257
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Why use virtual displacement to make constraint forces vanish?
Why do we use virtual displacement to vanish work done by constraint forces instead of the actual displacement?
2
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1
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142
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Example of a single constraint force doing virtual work despite the sum of work done by constraints being zero
When deriving d'Alembert's Principle it must be assumed, that the total virtual work done by constraint forces vanishes.
$$\sum_{j=1}^N\mathbf{C}_j\cdot\delta \mathbf{r}_j=0.$$
In the books I've read, ...
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D'Alembert's principle and the work done by constraint forces in Atwood's machine
From what I understand, constraint forces do no work because they are perpendicular to the allowed virtual displacements of the system. However, if you consider an unbalanced Atwood machine, in which ...
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Why the total virtual work done by forces from constraints vanishes? (Perpendicularity of two or more particles)
My mechanics book claims that the total force on the $i$-th particle is
$$
F_i=K_i+Z_i \tag{2.5}
$$where $Z_i$ is the force due to constraints and $K_i$ the real, dynamic force. Then, the book states ...
4
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1
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What does it mean for a force to 'produce' virtual displacement?
Book: Variational Principles of Mechanics by Lanczos, 1st edition, 1949.
Statement (page 80):
"Two systems of forces which produce the same virtual displacements are dynamically equivalent."...
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0
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Constraint forces do no virtual work: does this always apply?
The thread title is my main question, but to give some context, I'll include a particular example that made me ask the question in the first place.
In Hand and Finch, a small block is on a ...
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Why can we not set each applied force equal to zero?
With reference to page 17 of "Classical Mechanics" by Goldstein, Safko and Poole, the small paragraph after eq. 1.43,
$$\sum_i \mathbf{F}^{(a)}_i \cdot \delta \mathbf{r}_i ~=~ 0.\tag{1.43}$$
I do not ...
13
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The role of the virtual work principle
Lanczos' masterpiece "The Variational Principle of Mechanics" has, on page 76, the following statement:
Postulate A (virtual work): The virtual work of the forces of reaction is always zero for any ...
3
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2
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3k
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What is difference between variations of the work and virtual work?
I really want to know whether or not both equations are the same mathematically. I think that they are the same, I just want to be sure.
(Reference: this website.)
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Why does a system have to be holonomic?
So I'm doing some work from Taylor's mechanics book. He says for the problems in the book, we require the system to be holonomic - that is the number of generalized coordinates = number of Deg. of ...