All Questions
13
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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 ...
- 41
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0
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675
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Lagrangian intuition [duplicate]
I am new to lagrangian mechanics and it just baffles me the idea of subtracting potential energy from kinetic energy. Why don't we use kinetic energy alone and the least action path (between two ...
- 105
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 ...
- 468
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1
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257
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How is virtual work defined?
Let $S$ be a system with $g$ degrees of freedom, $\Sigma_g$ its configuration space and $\{q_i\}_{i=1}^g$ the lagrangian coordinates. If $P\in\Sigma_g$, we define a virtual displacement from $P$ as ...
- 1,989
1
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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?
- 11
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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9
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5
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2k
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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 ...
- 483
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4
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2k
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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 ...
- 1,335
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746
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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 ...
- 556
0
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1
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527
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Total work zero along the virtual displacement
I'm having some trouble understanding virtual work and displacement, especially a particular section of Goldstein. I'll use an example to explain my difficulty, but I realize this might be the product ...
- 2,849
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2
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167
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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 ...
- 21
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.)
- 41
2
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1
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329
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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 ...
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