Linked Questions

18 votes
4 answers
3k views

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 ...
0 votes
0 answers
128 views

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 ...
1 vote
0 answers
53 views

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 : ...
28 votes
3 answers
6k views

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 ...
  • 5,105
20 votes
1 answer
6k views

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.
19 votes
1 answer
5k views

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 ...
1 vote
1 answer
375 views

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 votes
2 answers
250 views

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 ...
2 votes
1 answer
166 views

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 ...
1 vote
2 answers
145 views

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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1 vote
1 answer
147 views

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 ...