Here... it's like this...
Person comes to me to ask for help on their transmission: I spoon feed. I give it them. I explain all steps. And do it for them becasue I respect their fundamental intelligence and KNOW they are not manipulating me. I know they just are stuck on putting pieces...
No, it just means YOU cannot help me. And that is OK.
I have learned a great deal from others here who took the time to step me through and not dispense information slowly.
I understand you probably teach this way and it probably works well for you and that is very good.
You are...
WWGD: you have helped me before, thank you.
Would you be willing to fill in the missing steps?
I make no excuses: my physics is bad -- I am a 56 year old engineer (I am very good at that, but my physics is bad).
I am not here for HW help. I am here to rapidly fill in gaps in my knowlege.
And...
Sorry again for all these ongoing question as I try to fix my math deficiencies. (Back to working on differential forms.)
So...
I understand that the equation of steepest ascent/descent in Cartesian coordinates is written:
dxi/dt = ∂f/∂xi
And I can follow the "physical interpretations" of...
Well, I am trying to say something like this... and I acknowledge I may be way off the mark.
If one throws a ball up with a force (not saying F=ma here... just force), the force maximizes the height.
(or minimizes the negative of the height).
But the height is weighted with the mass.
Second...
OK, so then no "explanation" in the traditional sense... how about just an interpretation along the lines of that link I posted.
Because that author comes really close to an interpretation. I just get muddled up on the "ball wants to" part.
And it would be great to hear that author's comment...
(Yes, I have searched the other posts and each one comes up deficient for what I want.)
Why must the Lagrangian be extremized? And why it is of the form L = T – V?
BUT I HAVE CAVEATS!
Please do it from first principles WITHOUT an understanding of F=ma.
(And, yes, I understand the calculus...
Marcus, may I? Comment on this please...We have a Lie Group which is a continuous group (and thus capable of modeling rotations -- sin, cos, etc.). The restriction of det=1 enables us to take the independent coordinates, equipped with the smoothness condition, and envision them as a manifold...
And you did it again... THANK YOU...
Here are my thoughts...
Something has gone very very wrong with math education for engineers.
I feel we are on the cusp of a new math (or may be you people already know that) but engineering is stuck for two reasons
1. The math they teach is old
2. The...
(Ode to Joy excerpt now playing loudly in my head.)
Wow... that was great...
You probably think this is silly and, in time, I may too. But right now, I need to hear someone say what you just said.
It takes a really kind and smart person to know where someone is being dense and how not to...
OK.. but I have read, time and time again now:
A lie group is a smooth manifold with a lot of symmetry
But you just wrote
A lie algebra is a smooth manifold with a lot of symmetry
I can see a lie group being smooth: SO(3) depends on continuous functions of rotations.
Now, I think I am hitting...