30 questions linked to/from Deriving the Lagrangian for a free particle
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### Why is the Lagrangian quadratic in $\dot{q}$? [duplicate]

My teacher said we only consider Lagrangians which are quadratic in $\dot{q}$, and we don't take other Lagrangians. I couldn't understand why. Can anyone please explain this?
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### Trouble understanding Landau & Lifshitz writing about Lagrangians and Galilean Relativity [duplicate]

We have two inertial coordinate systems, $K'$ and $K$. $K$ is moving with infinitesimal velocity ${\epsilon}$ relative to $K'$. Using Galilean relativity we can transform this into $v'=v+{\epsilon}$. ...
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### How does isotropy of free space imply $L(v^2)$ for a free particle? [duplicate]

From Mechanics; Landau and Lifshitz, it's stated on page 5: Since space is isotropic, the Lagrangian must also be indpendent of the direction of $\mathbf{v}$, and is therfore a function only of ...
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### Deriving the action and the Lagrangian for a free massive point particle in Special Relativity

My question relates to Landau & Lifshitz, Classical Theory of Field, Chapter 2: Relativistic Mechanics, Paragraph 8: The principle of least action. As stated there, to determine the action ...
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### Least-action classical electrodynamics without potentials

Is it possible to formulate classical electrodynamics (in the sense of deriving Maxwell's equations) from a least-action principle, without the use of potentials? That is, is there a lagrangian which ...
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### Proof that total derivative is the only function that can be added to Lagrangian without changing the EOM

So I was reading this: Invariance of Lagrange on addition of total time derivative of a function of coordiantes and time and while the answers for the first question are good, nobody gave much ...
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### Invariance of Lagrange on addition of total time derivative of a function of coordiantes and time

My question is in reference to Landau's Vol. 1 Classical Mechanics. On Page 6, the starting paragraph of Article no. 4, these lines are given: If an inertial frame $К$ is moving with an ...
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### How to determine the Lagrangian's “true” explicit dependence on time?

If your Lagrangian satisfies $$\frac{\partial \mathcal L}{\partial t} = 0$$ then you're happy, energy is conserved, etc. However, if the above doesn't hold, that doesn't necessarily mean energy ...
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### The form of Lagrangian for a free particle

I've just registred here, and I'm very glad that finally I have found such a place for questions. I have small question about Classical Mechanics, Lagrangian of a free particle. I just read Deriving ...