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### 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 ...
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### 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.
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...