Linked Questions
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D'Alembert's Principle: Necessity of virtual displacements
Why is the d'Alembert's Principle
$$\sum_{i} ( {F}_{i} - m_i \bf{a}_i )\cdot \delta \bf r_i = 0$$
stated in terms of "virtual" displacements instead of actual displacements?
Why is it so necessary ...
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What type of displacement is virtual displacement? Is it really a displacement? How to calculate it? [duplicate]
Searched this question a lot in different places but could not find any answer that could satisfy me. So I am here to clear my concepts regarding virtual displacement. Now I am clarifying my doubt.
As ...
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1
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D'Alembers Principle - further explanation [duplicate]
In question : Why is the d'Alembert's Principle formulated in terms of virtual displacements rather than real displacements in time? there is a response :
...
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28
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Are there examples in classical mechanics where D'Alembert's principle fails?
D'Alembert's principle suggests that the work done by the internal forces for a virtual displacement of a mechanical system in harmony with the constraints is zero.
This is obviously true for the ...
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Why can't d'Alembert's Principle be derived from Newton's laws alone?
The wiki article states that D'Alembert's Principle cannot derived from Newton's Laws alone and must stated as a postulate. Can someone explain why this is? It seems to me a rather obvious principle.
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19
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What is the definition of how to count degrees of freedom?
This question resulted, rather as by-product, the discussion on how to count degrees of freedom (DOF). I extend that question here:
Are necessary1 derivatives such as velocities counted as individual ...
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1
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Why is it important that there is no variation of time $\delta t=0$ in the definition of virtual displacement?
In Goldstein's Classical mechanics I found a proposition that I don't understand:
Similarly, the arbitrary virtual displacement $\delta \mathbf{r}_i$ can be connected with the virtual displacement $...
2
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2
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Time dependence of generalized coordinates and virtual displacement
The Cartesian coordinates of particles are related to the generalized coordinates via a transformation (for the $x$ component of the $j$-th particle) as:
$$x_j = x_j(q_1, q_2, \ldots, q_N, t)$$
What I ...
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2
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1
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Position in generalized coordinates
In Lagrangian mechanics, when talking about a particle position expressed in generalized coordinates it is usual to find the expression:
$$\mathbf{r}(q_0,...,q_k,t)\tag{1}$$
what it means this ...
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2
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About virtual displacement
Thornton Marion
The varied path represented by $\delta y$ can be thought of physically as a virtual displacement from the actual path consistent with all the forces and constraints (see Figure above)....
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D'Alembert derivation of Lagrange Equation - why can it use both virtual and normal differentials?
In "Classical Mechanics" by Goldstein and "A Students Guide to Lagrangians and Hamiltonians" by Hamill I noticed that both the virtual displacement derivatives and the normal displacement derivatives ...
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