Someone
Reputation
Top tag
Next privilege 125 Rep.
Vote down
1 5
Impact
~5k people reached

• 0 posts edited
• 0 helpful flags
• 1 vote cast

# 13 Actions

 Sep 14 awarded Notable Question Apr 22 awarded Popular Question Mar 30 awarded Nice Question Apr 11 awarded Supporter Apr 11 awarded Scholar Apr 11 accepted Deriving the Lagrangian for a free particle Apr 11 comment Deriving the Lagrangian for a free particle @Qmechanic, thanks a lot for such a detailed update! You derived the form of $L$ from the condition that the equations should not change, which is a weaker condition than $\Delta L$ being a time derivative, as far as I know. So my last question is why did you mention that form-invariance implies $\Delta L$ being a time derivative? I looked up Noether's theorem, but didn't find there an answer. Could you please point out to me, from where exactly does that statement about $\Delta L$ follow? And why did you even mention it, since you used the condition of form-invariance? Apr 2 comment Deriving the Lagrangian for a free particle @altertoby, I didn't understand your argument, as $$4v^3=\text{const}$$ seems to imply $v=\text{const}$ (one dimentional case). In 3 dimensions it would be $$4v^2{\bf v}=\text{const},$$ what lead me to the same result ($v_i^3=\text{const}$). Also, how can $v$ (hence ${\bf v}$ as well) have no physical meaning? Would ${\bf v}$ not had the meaning of velocity, how could we apply the Galileo's relativity principle and come to the conclusion that $L=L(v^2)$? Apr 1 comment Deriving the Lagrangian for a free particle Finally, did I get it right that Landau only proved, that $\frac{m v^2}{2}$ will fit the requirements? Is there a proof that this is the only possible expression? Apr 1 comment Deriving the Lagrangian for a free particle Thank you, the first question is now clear! It's a shame, the authors didn't bother to mention the smoothness there. But I'm still confused with the second part. I didn't find a clear definition of form-invariance here. Does form-invariance mean that the families of solutions will be the same? If so, do there exist second-order DEs that generate the same sets of solutions, but are different (linear-independent)? Apr 1 awarded Student Mar 31 revised Deriving the Lagrangian for a free particle Tags are now more relevant. Mar 31 asked Deriving the Lagrangian for a free particle