Timeline for Derivatives of the lagrangian of generalized coordinates [closed]

11 events

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Dec 12, 2022 at 21:57	comment	added	rannasquaer		@MichaelSeifert wow, that makes sense, because otherwise one derivative cancels out and the other will be 1
Dec 12, 2022 at 21:55	comment	added	rannasquaer		@schris38 I'm reading Classical Dynamics of Particles and Systems by Marion
Dec 12, 2022 at 21:51	history	edited	rannasquaer	CC BY-SA 4.0	added 385 characters in body
Dec 12, 2022 at 14:28	history	closed	Farcher Michael Seifert Miyase		Not suitable for this site
Dec 12, 2022 at 12:43	answer	added	basics		timeline score: 0
Dec 12, 2022 at 12:39	comment	added	Michael Seifert		In your expression, you have the same index ($k$) as a "dummy" index in your sum and as a "free" index attached to the $q$ you'r taking the derivative of. Don't do that. Before taking these derivatives, you should always relabel your dummy indices so that they don't conflict with the free indices. So you should really have $$ \frac{\partial U}{\partial q_k} = \frac{\partial}{\partial q_k} \left(\frac{1}{2} \sum_{j,l} A_{jl} q_j q_l \right) $$ and similarly for $\partial T/\partial \dot{q}_k$.
Dec 12, 2022 at 12:37	review	Close votes
Dec 12, 2022 at 14:28
Dec 12, 2022 at 12:34	comment	added	schris38		What are you reading?
Dec 12, 2022 at 12:22	history	edited	Qmechanic♦		edited tags
S Dec 12, 2022 at 12:10	review	First questions
Dec 12, 2022 at 13:26
S Dec 12, 2022 at 12:10	history	asked	rannasquaer	CC BY-SA 4.0