Linked Questions

22
votes
5answers
4k views

Is there a proof from the first principle that the Lagrangian L = T - V?

Is there a proof from the first principle that for the Lagrangian $L$, $$L = T\text{(kinetic energy)} - V\text{(potential energy)}$$ in classical mechanics? Assume that Cartesian coordinates are ...
11
votes
1answer
4k views

Deriving D'Alembert's Principle

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.
7
votes
4answers
7k views

Can internal forces do work?

My Mechanics textbook claims that the sum of the work by internal forces is not generally zero. translated to English the paragraph reads: Notice about the work by internal forces: the work by the ...
4
votes
2answers
9k views

Euler-Lagrange equations and friction forces

We can derive Lagrange equations supposing that the virtual work of a system is zero. $$\delta W=\sum_i (\mathbf{F}_i-\dot {\mathbf{p}_i})\delta \mathbf{r}_i=\sum_i (\mathbf{F}^{(a)}_i+\mathbf{f}_i-\...
9
votes
1answer
2k views

When is the principle of virtual work valid?

The principle of virtual work says that forces of constraint don't do net work under virtual displacements that are consistent with constraints. Goldstein says something I don't understand. He says ...
5
votes
1answer
1k views

A Question about Virtual Work related to Newton's Third Law

In describing D'Alembert's principle, the lecture note I was provided with states that the total force $\mathbb F_l$ acting on a particle can be taken as, $$\mathbb F_l=F_l+\sum_mf_{ml}+C_l,$$ ...
2
votes
3answers
1k views

Must the Lagrangian always be known for the Euler-Lagrange equations to be of any use?

When studying classical mechanics using the Euler-Lagrange equations for the first time, my initial impression was that the Lagrangian was something that needed to be determined through integration of ...
5
votes
2answers
1k views

The Equivalency of Newton's Second Law, Hamilton's Principle and Lagrange Equations [closed]

Consider the following question in classical mechanics Are Newton's Second Law, Hamilton's Principle and Lagrange Equations equivalent for particles and system of particles? If Yes, where ...
2
votes
1answer
2k views

Why friction force is force of constraint?

My understanding about constraint force is that it is a force which limits the geometry of particle's motion. For example, situations such as the particle trapped in a track or limited in domain can ...
2
votes
2answers
629 views

D'Alembert Principle Intuitive Understanding

Does Alembert work for systems of rigid bodies? My question comes from this image. (sorry for the poor drawing!) I'm trying to find the acceleration of the block exclusively from the sum of ...
4
votes
3answers
333 views

Why is the d'Alembert's Principle formulated in terms of virtual displacements rather than real displacements in time? [duplicate]

Why is the d'Alembert's Principle formulated in terms of virtual displacements rather than real displacements in time? EDIT In other words, which step of the derivation of D'Alembert's principle (or ...
0
votes
1answer
544 views

“Principle of least action” and “Principle of conservation of energy”: Which one is fundamental and which one is derived? [closed]

Suppose I throw a ball upwards. First it will rise under gravity and then fall under gravity. During the rising part the kinetic energy gradually decreases and the potential energy increases until ...
0
votes
2answers
323 views

Why is it difficult to understand the phenomena of chaos in Newtonian mechanics?

This is a very simple-minded question. Why is it difficult to understand the phenomena of chaos in Newtonian mechanics and one has to turn to Hamiltonian formulation? I haven't read much about chaos ...